Fleming received a Ph.D. in Mathematics from the University of Wisconsin in 1951. After holding positions at the RAND Corporation and Purdue University, he joined the faculty of Brown University in 1958. He chaired the Mathematics Department at Brown from 1965-1968 and the Division of Applied Mathematics from 1982-1985 and 1991-94. In 1995, he became University Professor Emeritus.
Fleming is the author of more than 125 research articles and three books. The topics of his research have included: calculus of variations, geometric measure theory, stochastic control, differential games, mathematical genetics models, measure valued stochastic processes, nonlinear filtering, and mathematical finance.
Honors which Fleming has received include a NSF Senior Postdoctoral Fellowship and a Guggenheim Fellowship. He received a Steele Prize from the American Mathemetical Society and a Reid Prize from the Society of Industrial and Applied Mathematics. He also received an honorary Doctor of Science degree from Purdue University, and is a member of the American Academy of Arts and Sciences.
A stochastic control model of investment, production and consumption, (with T. Pang) Quarterly of Applied Math. 63 (2005) 71-87.
Max-plus approaches to continuous space control and dynamic programming, in Idempotent Mathematics and Mathematical Physics (G.L. Litvinov and V.P. Maslov eds.) American Math. Soc. Contemporary Math. No. 377, 2005, pp. 145-160. February 2006
Optimal investment models with minimum consumption criteria, Australian Economic Papers, December 2005, 307-321.
The tradeoff between consumption and investment in incomplete Þnancial markets (with D. Hernandez-Hernandez), Applied Math. Optim. 52 (2005) 219-234.
Stochastic optimal control, international Þnance and debt, (with J.L. Stein), J. Banking and Finance 28 (2004) pp. 979-996.
An application of stochastic control theory to Þnancial economics, (with T. Pang) SIAM J. Control Optimiz. 43 (2004) 502-531.
Max-plus stochastic processes and control, submitted to Applied Math. Optim. 49 (2004) 159-181.
An application of stochastic control theory to Þnancial economics, (with T. Pang) SIAM J. Control Optimiz. 43 (2004) 502-531.
An optimal consumption model with stochastic volatility, (with D. Hernandez-Hernandez) Finance and Stochastics, 7 (2003) 245-262.
Max-plus linear partial differential equations, Research Directions in Distributed Parameter Systems, (eds. R.C. Smith and M.A. Demetriou) SIAM Publications, 2003, pp. 123-137.
Some optimal investment, production and consumption models, Proc. Snowbird Math. of Finance Conf. (G. Yin and Q. Zhang eds.) American Math. Soc. Contemporary Math. No. 351, 2003, pp. 115-123.
An optimal consumption-investment problem for factor-dependent models, (with Daniel Hernandez-Hernandez) Proc. Conf. on Stochastic Theory and Control (B. Pasik-Duncan ed.) Springer LN Control Info. Sci. No. 280, 2002, pp. 121-130.
Risk sensitive control and an optimal investment model II, (with S.-J. Sheu), Annals Appl. Probab. 12 (2002) 730-767.
Max-plus stochastic control, Proc. Conf. on Stochastic Theory and Control (B. Pasik-Duncan ed.) Springer LN Control Info. Sci. No. 280, 2002, pp. 111-119.
Stochastic control models of optimal investment and consumption, Aportaciones Matematicas, vol. 16, 2001. Sociedad Matematica Mexicana, pp. 159-203.
Stochastic optimization in discrete time, (with J.L. Stein), in Economic Theory Dynamics and Markets: Essays in Honor of Ryuzo Sato, Kluwer Academic Publishers, 2001.
Deterministic and stochastic approaches to nonlinear filtering, (with W.M. McEneaney) in Math. Control Signals Systems, 14 (2001), pp. 109-142.
An infinite horizon risk sensitive control problem (with S.-J. Sheu), in Optimal Control and Partial Differential Equations (J.L. Menaldi, E. Rofman, A. Sulem eds) IOS Press, 2001, pp. 521-529.
Deterministic and stochastic approaches to nonlinear Þltering, in System Theory: Modelling, Analysis and Control, (T.E. Djaferis and I.C. Schick eds) Kluwer Academic Publishers, 2000, pp. 121-130.
A max-plus based algorithm for an HJB equation of nonlinear Þltering, (withW.M.McEneaney) SIAM J. on Control and Optimiz., 38 (2000) 683-710.
Deterministic and stochastic approaches to nonlinear Þltering, in System Theory: Modelling, Analysis and Control, (T.E. Djaferis and I.C. Schick eds) Kluwer Academic Publishers, 2000, pp. 121-130.
A max-plus based algorithm for an HJB equation of nonlinear Þltering, (withW.M.McEneaney) SIAM J. on Control and Optimiz., 38 (2000) 683-710.
Risk sensitive control and an optimal investment model, (with S.-J. Sheu) Math. Finance 10 (2000) 197-213.
Risk sensitive control of Þnite state machines on an inÞnite horizon II, (with D. Hernandez-Hernandez), SIAM J. on Control Optimiz., 37 (1999) 1048-1069.
Controlled Markov processes and mathematical Þnance, in Nonlinear Analysis Differential Equations and Control, (ed. F.H. Clarke and R.J. Stein), Kluwer Academic Publishers, NATO Science Series C: Math. Phys. Sci. Vol. 528, (1999), pp. 407-446.
Risk sensitive control of Þnite state machines on an inÞnite horizon II, (with D. Hernandez-Hernandez), SIAM J. on Control Optimiz., 37 (1999) 1048-1069.
Controlled Markov processes and mathematical Þnance, in Nonlinear Analysis Differential Equations and Control, (ed. F.H. Clarke and R.J. Stein), Kluwer Academic Publishers, NATO Science Series C: Math. Phys. Sci. Vol. 528, (1999), pp. 407-446.
Risk-sensitive production planning of a stochastic manufacturing system, (with Q. Zhang) SIAM J. on Control and Optimiz., 36 (1998) 1147-1170.
Optimal long term growth rate of expected utility of wealth, (with S.-J. Sheu) Ann. Appl. Prob. 9 (1998) 871-903.
Risk sensitive production planning (with Q. Zhang) Proc. 37th IEEE Conf. on Decision and Control, Dec. 1998.
Risk sensitive control of Þnite state machines on an inÞnite horizon I (with D. Hernandez-Hernandez) Proc. 36th IEEE Conf. on Decision and Control, Dec. 1997.
Some results and problems in risk sensitive stochastic control, Computational and Applied Math. 16 (1997) 99-115.
Risk sensitive control of Þnite state machines on an inÞnite horizon I (with D. Hernandez-Hernandez) Proc. 36th IEEE Conf. on Decision and Control, Dec. 1997.
Risk sensitive and robust nonlinear Þltering (with W.M. McEneaney) Proc. 36th IEEE Conf. on Decision and Control, Dec. 1997.
Risk sensitive control of finite state machines on an inÞnite horizon I, (with D. Hernandez-Hernandez) SIAM J on Control and Optimiz., 35 (1997) 1790-1810.
Asymptotics for the principal eigenvalue and eigenvector of a nearly Þrst order operator with large potential, (with S.-J. Sheu) Annals of Probab., 25 (1997), 1953-1994.
Risk sensitive control of Þnite state machines on an inÞnite horizon I (with D. Hernandez-Hernandez) Proc. 36th IEEE Conf. on Decision and Control, Dec. 1997.
Risk sensitive control of finite state machines on an inÞnite horizon I, (with D. Hernandez-Hernandez) SIAM J on Control and Optimiz., 35 (1997) 1790-1810.
Asymptotics for the principal eigenvalue and eigenvector of a nearly Þrst order operator with large potential, (with S.-J. Sheu) Annals of Probab., 25 (1997), 1953-1994.
Deterministic nonlinear Þltering, Annali Scuola Normale Superiore Pisa, Sci. Fis. Matem. Se 4 25 (1997) 435-454.
Risk sensitive and robust nonlinear Þltering (with W.M. McEneaney) Proc. 36th IEEE Conf. on Decision and Control, Dec. 1997.
Optimal investment models and risk sensitive stochastic control, in IMA Volumes in Math and Applic. No. 65, 1995 pp 75-88.
Risk sensitive control on an inÞnite time horizon, (with W. M. McEneaney) SIAM J. on Control and Optimization 33 (1995) 1881-1915.
Risk sensitive control on an inÞnite time horizon, (with W. M. McEneaney) SIAM J. on Control and Optimization 33 (1995) 1881-1915.
The risk-sensitive index and the H2 and H∞ norms for nonlinear systems, (with M.R. James) Math. of Control, Signals and Systems 8 (1995) 199-221.
Numerical methods for infinite horizon risk sensitive stochastic control (with J. Yang), Proc. 33rd IEEE Conf. on Decision and Control, Dec. 1994.
Controlled Markov Processes and Viscosity Solutions, (with H. M. Soner) Springer-Verlag, 1992; Second Edition, 2006.
Asymptotic series and exit time probabilities, (with M. James) in Annals of Probability 20 (1992) 1369-1384.
Stochastic control and large deviations, Springer Lecture Notes in Computer Sciences, No. 653, 1992, pp 291-300. INRIA 25th Anniversary Conference Volume.
Risk sensitive control with ergodic cost criteria (with W. M. McEneaney) Proc. 31st Conf. on Decision and Control, Dec. 1992.
Control and Info. Sci. No. 184, 1992, pp. 185-187.
Piecewise monotone Þltering with small observation noise, (with Q. Zhang) Proc. Joint US - France Workshop on Stochastic Analysis (eds. I. Karatzas and D. Ocone) April 1991.
An optimal investment/consumption model with borrowing, (with T. Zariphopoulou) Math. Oper. Res. 16 (1991) 802-822.
Risk sensitive optimal control and differential games (with W. M. McEneaney) Proc. Conf. on Adaptive and Stochastic Control, University of Kansas, 1991, Springer Lecture Notes on
Piecewise monotone Þltering in discrete time with small observation noise, (with D. Ji, P. Salame and Q. Zhang) IEEE Trans. Auto. Control 36 (1991) 1181-1185.
Piecewise monotone Þltering with small observation noise, (with Q. Zhang) Proc. Joint US - France Workshop on Stochastic Analysis (eds. I. Karatzas and D. Ocone) April 1991.
Piecewise monotone Þltering in discrete time with small observation noise, (with D. Ji, P. Salame and Q. Zhang) IEEE Trans. Auto. Control 36 (1991) 1181-1185.
Nonlinear Þltering with small observation noise: piecewise monotone observations, (with Q. Zhang) in Stochastic Analysis, eds. E. Merzbach, A. Schwartz and E. Mayer-Wolf. Academic Press (1991) 153-168.
Numerical method for an optimal investment/consumption problem, (with B. Fitzpatrick) in Math. Oper. Res. (1991) 823-841.
Numerical methods for optimal investment-consumption model (with B. Fitzpatrick) Proc. 29th Conf. on Decision and Control, Dec. 1990.
Piecewise monotone Þltering with small observation noise, (with E. Pardoux) SIAM J. on Control and Optimiz. 27 (1989) 1156-1181.
Value Functions for Two-Player, Zero-Sum Stochastic Differential Games, (with P.E. Souganidis), Indiana University Math J. 38 (1989) 293-312.
Convex Duality Approach to the Optimal Control of Diffusions, (with D. Vermes), SIAM J. on Control and Optimization 27 (1989) 876-907.
Asymptotic Expansions for Markov processes with Levy Generators, (with H.M. Soner), Applied Math. and Optimiz. 19 (1989) 203-223.
Generalized solutions and convex duality in optimal control in Partial Differential Equations and the Calculus of Variations, (ed F. Colombini et al), Birkhauser, 1989, pp 461-472
Info. Sci Vol. 111 (1988) 725-739.
Two-Player, Zero-Sum Stochastic Differential Games (with P.E. Souganidis), Analyse Mathematique et Applications, Gauthier-Villars, 1988.
Piecewise Monotone Filtering With Small Observation Noise (with E. Pardoux), Proc. 27th Conf. on Decision and Control, Dec. 1988.
Stochastic Differential Systems, Stochastic Control Theory and Applications, (co-editor with P.L. Lions) IMA Volumes in Math. and Its Applications No. 10, Springer-Verlag, 1987.
Controlled Markov Processes and Nonlinear Evolution Equations, Accademia Nazionale dei Lincei, Scuola Normale Superiore, 1987.
An Optimal Stochastic Production Planning Problem with Randomly Fluctuating Demand,(with S.P. Sethi and H.M. Soner), SIAM J. on Control and Optimization 25 (1987). 1494-1502.
On the Existence of the Dominant Eigenvalue and its Application to the Large Deviation Properties of an Ergodic Markov Process, (with S. J. Sheu and H.M. Soner), Stochastics 22 (1987) 187-199.
Asymptotic Series and the Method of Vanishing Viscosity, (with P.E. Souganidis), Indiana Univ. Math. J. 35 (1986) 425-447.
A PDE Approach to Asymptotic Estimates for Optimal Exit Probabilities, (with P. E. Souganidis), Annali della Scuola Normale Superiore Pisa, Ser. IV 23 (1986) 171-192.
Generalized Solutions in the Optimal Control of Diffusions (with D. Vermes), Proc. IMA Workshop, June 1986, IMA Vols. in Math. and Applic. No. 10, Springer-Verlag, 1987.
A Stochastic Production Planning Problem with Random Demand, (with H.M. Soner) Proc. 24th IEEE Conf. on Decision and Control, Vol. 1, Ft. Lauderdale, Florida, December 11-13, 1985.
Recent Advances in Dynamic Programming, (co-editor with I. Capuzzo-Dolcetta and T. Zolezzi), Springer Lecture Notes in Math, No. 1119, 1985.
Stochastic Variational Formula for Fundamental Solutions of Parabolic PDE, (with S-J. Sheu), Applied Math and Optimization, 13 (1985).
Asymptotic Series for Solutions to the Dynamic Programming Equation for Diffusions with Small Noise, (with P.E. Souganidis) Proc. 24th IEEE Conf. on Decision and Control, Ft. Lauderdale, Florida, December 11-13, Vol. 1, 1985.
A Stochastic Control Approach to Some Large Deviations Problems, Proc. Conference on Recent Advances in Dynamic Programming, Rome, March 1984. Springer Lecture Notes in Math. No. 1119, 52-66.
On Stochastic Relaxed Controls for Partially Observed Diffusions, (withM.Nisio), OsakaMath. J. 93 (1984) 71-108.
Optimal Control of Markov Processes, Proc. Intl. Congress of Mathematicians 1983 (invited Plenary Address).
Stochastic Calculus of Variations and Mechanics, J. Optimiz. Theory Applic., 41 (1983) 55-74.
A Regular Perturbation Expansion in Nonlinear Filtering, (withR.W.McGwier), Proc. 22nd IEEE Conf. on Decision and Control, December 1983, pp. 82-83.
Optimal control and Nonlinear Filtering for Nondegenerate Diffusion Processes, (with S.K. Mitter), Stochastic 7 (1982) 63-77.
Optimal Control for Partially Observed Diffusions, (with E. Pardoux), SIAM J. on Control and Optimization, 20 (1982) 261-285.
Logarithmic Transformations and Stochastic Control, in Advances in Filtering and Optimal Stochastic Control, Springer Lecture Notes on Control and Information Sciences No. 42 (1982) 131-142.
Advances in Filtering and Optimal Stochastic Control, (co-editor with L.G. Gorostiza), Springer Lecture. Notes in Control and Information Sciences, No. 42 (1982).
Nonlinear Semigroup for Controlled Partially Observed Diffusions, SIAM. J. on Control and Optimization, 20 (1982) 286-301.
Optimal Control and Nonlinear Filtering of Nondegenerate Diffusions, (with S.K. Mitter), Proc. 20th IEEE Conf. on Decision and Control, December 1981.
Control Optimo de Processos de Diffusion Markovians, (with O. Hernandez Lerma) Conferencias sobre sistemas estocasticas, Ciencia 32 (1981) 39-55.
Optimal Exit Probabilities and Differential Games, (with C-P Tsai), Applied Math. and Optimization, 7 (1981).
Stochastic Control Under Partial Observations, 4th Intl. Conf. on Analysis and Optimization of Systems, INRIA, France, December 1980.
Measure-valued Processes in the Control of Partially Observable Stochastic Systems, Applied Math. and Optimization, 6 (1980) 271-285.
Lecture Notes on Diffusion Approximation and Optimal Stochastic Control, Clemson University, 1979.
Some Measure-valued Markov Processes in Population Genetics Theory, (with M. Viot), Indiana Univ. Math. J., 28 (1979), 817-844.
Partially Observed Stochastic Control systems, (with E. Pardoux), Proc. 18th IEEE Conf. on Decision and Control, December 1979, pp. 163-165.
Minimum Exit Probabilities and Differential Games, (with C.P. Tsai), Proc. 3rd Kingston Conference on Differential Games and Control Theory, Marcel Dekker, 1979.
Equilibrium Distributions of Continuous Polygenic Traits, SIAM J. Appl. Math., 36 (1979), 148-168.
Exit Probabilities and Optimal Stochastic Control, Applied Math. and Optimization, 4 (1978) 329-346.
Some Measure-valued Population Processes, (with M. Viot), in Stochastic Analysis, A. Friedman and M. Pinsky, Eds., Academic Press (1978) 97-108.
Large Deviations for Diffusions Depending on Small Parameters: A Stochastic Control Method, Proc. 1st AFCET-SMF Symposium, Ecole Polytechnique, September 1978.
Optimal Control of Markov Diffusion Processes, Proc. Joint Automatic Control Conference, Vol. 1, October 1978, pp. 355-358.
Optimal Inclusion Probability and Differential Games, (with C.P. Tsai), IRIA Seminars Review, 1977.
Generalized Solutions in Optimal Stochastic Control, Proc. Second Kingston Conf. on Differential Games, Marcel Dekker, 1977.
Inclusion Probability and Optimal Stochastic Control, IRIA Seminars Review, 1977.
Some Stochastic Systems Depending on Small Parameters, (with C.P. Tsai), Proc. Intl. Symposium on Dynamical Systems at Brown University, Academic Press (1976) 103-114.
Diffusion Processes in Population Biology, Applied Probability, 7 (1975) 100-105.
Distributed Parameter Systems in Population Biology, in Control Theory, Numerical Methods and Computer systems Modeling, pp. 179-191, A. Bensoussan and J.L. Lions, Eds., Lecture Notes in Econ. andMath. Systems, 107 (1975) Springer-Verlag.
Deterministic and Stochastic Optimal Control, (with R.W. Rishel), Springer-Verlag, 1975.
A Selection-migration Model in Population Genetics, J. Math, Biology, 2 (1975) 219-233.
Some One Dimensional Migration Models In Population Genetics Theory, (with C.H. Su). Theo. Popn. Biol. 5 (1974) 431-449.
Optimal Control of Diffusion Processes, in Stochastic Differential Equations, J.B. Keller, H.P. McKean, Eds., SIMA-AMS Proc., Vol. VI (1973) 163-171.
Dynamical Systems with Small Stochastic Terms, in Techniques of Optimization, A.V. Balakrishnan, Ed., Academic Press (1972) 325-334.
Stochastically Perturbed Dynamical Systems, Proc. Conf. on Stochastic Differential Equations, Edmonton, July 1972. Rocky Mountain Mathematical Journal, 4 (1974) 407-433.
Stochastic Control for Small Noise Intensities, SIAM J. Control 9 (1971), 473-517.
Optimal Continuous Parameter Stochastic Control, in Actes du Congress Int'l. des Math. 1970, Gauthier-Villars, Park 3 (1971) 163-167.
Nonlinear Partial Differential Equations: Probabilistic and Game Theoretic Methods, Proc. CIME Summer School "Problems in Nonlinear Analysis", Varenna, August 1970, pp. 95.
Nonlinear Partial Differential Equations: Probabilistic and Game Theoretic Methods, Proc. CIME Summer School "Problems in Nonlinear Analysis", Varenna, August 1970, pp. 95.
The Cauchy Problem for a Nonlinear First-Order Partial Differential Equation, J. Differential Equations 5(1969) 515-530.
Optimal Continuous Parameter Stochastic Control, SIAM Review 11 (1969) 470-509.
Controlled Diffusions Under Polynomial Growth Conditions, in Calculus of Variations and Control Theory, A.V. Balakrishnan, ed., Academic Press, New York, 1969, 209-234.
Optimal Control of Partially Observable Diffusions, SIAM J. Control 6 (1968), 194-214.
Some Problems of Optimal Stochastic Control, in Stochastic Optimization and Control, H.F. Karreman Ed., John Wiley, New York (1968) 59-64.
Stochastic Lagrange Multipliers, Mathematical Theory of Control, Proc. Symp., Univ. of Southern California, 1967, Academic Press, New York (1967) 443.
Duality and a priori Estimates in Markovian Optimization Problems, J. Math. Anal. Appl 16 (1966), 254-279; Erratum, ibid. 19 (1966) 204.
Flat Chains Over a Finite Coefficient Group, Trans. American Math. Society, 121 (1966) 160-186.
Optimal Control of Diffusion Processes, in Functional Analysis and Optimization, E.R. Cainiello Ed., Academic Press, (1966) 68-84.
On the Existence of Optimal Stochastic Controls, (with M. Nisio), J. Mathematics and Mechanics 15 (1966), 777-794.
Functions of Several Variables, Addison-Wesley, 1965, 2nd ed., Springer-Verlag, 1977.
The Cauchy Problem for Degenerate Quasilinear Parabolic Equations, J. of Mathematics & Mechanics, 13 (1964) 987-1008.
The Convergence Problem for Differential Games II, Contributions to the Theory of Games, 5, Princeton University Press, 1964.
Some Markovian Optimization Problems, J. of Mathematics & Mechanics, 12, No. 1 (1963)131-140.
A Problem of Random Accelerations, Report No. 403, University of Wisconsin Math. Research Center, 1963.
On the Oriented Plateau Problem, Rendiconti Circolo Mat. Palermo (2), 11, (1962) 1-22.
The convergence Problem for Differential Games, J. Math. Analysis & Applic., 3 (1961) 102-116.
Normal and Integral Currents, (with H. Federer), Annals of Mathematics, 72 (1960) 458-520.
An Integral Formula for Total Gradient Variation, (with R. Rishel), Archiv der Math., 11 (1960) 218-222.
Functions whose Partial Derivatives are Measures, Illinois Journal of Mathematics, 4 (1960), 452-478.
Nondegenerate Surfaces and Fine-Cyclic Surfaces, Duke Mathematical Journal, 26 (1959) 137-146.
Nondegnerate Surfaces of Finite Topological Type, Trans. American Mathematical Society, 90 (1959) 323-335.
Functions with Generalized Gradient and Generalized Surfaces, Annali di Mat. Ser. 4, 46 (1957), 93-104.
Irreducible Generalized Surfaces, Rivista Mat. Univ. Parma, 8 (1957) 251-281.
An Example in the Problem of Least Area, Proc. American Mathematical Society, 7 (1956) 1063-1974.
Variational Problems with Constraints, (with R. Bellman and D.V. Widder). Annali di Mat. (4), 41 (1956) 301-323.
Representations of Generalized Surfaces as Mixtures, (with L.C. Young), Rendiconti Circolo Mat. Palermo (2), 5 (1956) 117-144.
Generalized Surfaces with Prescribed Elementary Boundary, (with L.C. Young), Rendiconti Circolo Mat. Palermo (2), 5 (1956) 320-340.
A Generalized Notion of Boundary, (with L. C. Young), Trans. American Mathematical Society, 76 (1954) 457-484.
On a Class of Games over Function Space and Related Variational Problems, Annals of Mathematics, 60 (1954) 578-594.
Optimal investment-consumption models in international Þnance, (with J.L. Stein) unpublished preprint.
Hedging in incomplete markets with HARA utility, (with D. Duffie, H. M. Soner and T. Zariphopoulou) to appear in the J. of Economic Dynamics and Control.
A Note on Differential Games of Prescribed Duration, Contrib. Theory of Games, 3, Annals of Mathematics Studies, No. 39, pp.407-412.
Piecewise Linear Filtering With Small Observation Noise (with D. Ji and E Pardoux), Proc. 8th INRIA Conf. on Analysis & Optimiz of Systems, Springer Lecture Notes in Control and
On Differential Games with an Integral Payoff, (with L.D. Berkovitz), Contrib. Theory of Games, 3, Annals of Mathematics Studies No. 39, pp.413-435.
Optimal portfolio rebalancing with transactions costs, (with S. Grossman, J-L. Vila and T. Zariphopoulou), preprint.
A PDE Approach to Asymptotic Estimates for Optimal Exit Probabilities, (with P. E. Souganidis), Springer Lecture Notes in Control and Information Science, Proc. IFIP Conf., Marseille,
Year | Degree | Institution |
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1951 | PhD | University of Wisconsin |