Paul G. Dupuis IBM Professor of Applied Mathematics

Brown Affiliations

Research Areas

scholarly work

Dynamic importance sampling for uniformly recurrent Markov chains (with H. Wang), Annals of Applied Probability, 15, (2005), 1—38.

On the convergence from discrete to continuous time in an optimal stopping problem (with H. Wang), Annals of Applied Probability 15, (2005), 1339-1366.

Importance sampling, large deviations and differential games (with H.Wang), Stochastic and Stochastics Reports, 76, (2004), 481—508.

Large deviation asymptotics for occupancy problems (with Carl Nuzman and Phil Whiting), Annals of Probab., 32, (2004), 2765—2818.

Explicit solutions for a network control problem in the large deviation regime (with Rami Atar and Adam Shwartz), QUESTA, 46, (2004), 159—176.

An escape time criterion for queueing networks: Asymptotic risk-sensitive control via differential games (with Rami Atar and Adam Shwartz), Math. of OR., 28, (2003), 801—835.

Large deviations for the empirical measures of reflecting Brownian motion and related constrained processes in IR+ (with A. Budhiraja), Elec. J. of Probab., 8, (2003), 1—46.

Explicit solution to a robust queueing control problem, SIAM J. on Control and Opt., 23, (2003), 1854—1875.

Optimal stopping with random intervention times (with H. Wang), Adv. Applied Probability, 34, (2002), 1—17.

Second order numerical methods for first order Hamilton-Jacobi equations (with A. Szpiro), SIAM J. on Numerical Analysis, 40, (2002) pp. 1136—1183.

A differential game with constrained dynamics and viscosity solutions of a related HJB equation (with R. Atar), Nonlinear Analysis: Theory, Methods and Applications, 55, (2002) pp. 1105—1130.

A time-reversed representation for the tail probabilities of stationary reflected Brownian motion (with K. Ramanan), Stoch. Proc. and Their Appl., 98, (2002), pp. 253—287.

Numerical Methods for Stochastic Control Problems in Continuous Time (with H. J. Kushner), Second Revised Edition, Springer-Verlag, New York, 2001.

On positive recurrence of constrained diffusion processes (with R. Atar and A. Budhiraja), Ann. of Probab. 29 (2001), 979—1000.

Risk-sensitive and robust escape control for degenerate processes (with M. Bou´e), Math. of Control, Signals and Systems, 14 (2001) pp. 62—85.

Convergence of the optimal feedback policies in a numerical method for a class of deterministic optimal control problems (with A. Szpiro), SIAM J. on Control and Opt., 40 (2001) pp. 393—420.

An explicit formula for the solution of certain optimal control problems on domains with corners (with K. Ramanan) an invited paper in the special issue of Probab. Th. and Math. Stat. dedicated to A. Skorokhod 63, (2000), pp. 32—48.

A variational representation for positive functionals of infinite dimensional Brownian motion (with A. Budhiraja), Prob. Math. Statist. 20 (2000) pp. 39—61.

Large deviations for small noise diffusions with discontinuous statistics (with M. Bou´e and R. S. Ellis), Prob. Theor. and Rel. Fields 116 (2000) pp. 125—148.

Robust properties of risk—sensitive control (with M. R. James and I. R. Petersen), Math. of Control, Signals and Systems. 13 (2000) pp. 318—332.

Minimax optimal control of stochastic uncertain systems with relative entropy constraints (with I. R. Petersen and M. R. James), IEEE Trans. on Auto. Control. 45 (2000) pp. 398—412.

A multiclass feedback queueing network with a regular Skorokhod Problem (with K. Ramanan), Queueing Systems, 36 (2000) pp. 327—349.

Large deviations and queueing networks: methods for rate function identification (with R. Atar), Stoch. Proc. and Their Appl. 84 (1999) pp. 255—296.

Simple necessary and sufficient conditions for the stability of constrained processes (with A. Budhiraja), SIAM J. on Applied Math. 59 (1999), pp. 1686—1700.

Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control (with M. Bou´e), SIAM J. on Numerical Analysis 36 (1999), pp. 667—695.

Convex duality and the Skorokhod Problem, parts I and II (with K. Ramanan), Prob. Th. and Rel. Fields, 115 (1999), pp. 153—195 and 115 (1999), pp. 197—236.

A variational formulation of a problem in image matching (with U. Grenander and M. Miller), Quarterly of Applied Mathematics, 56 (1998), pp. 587—600.

A Skorokhod Problem formulation and large deviation analysis of a processor sharing model (with K. Ramanan), Queueing Systems, 28 (1998), pp. 109—124.

Large deviation properties of data streams that share a buffer (with K. Ramanan), The Annals of Applied Probability 8, (1998), pp. 1070—1129.

A variational representation for certain functionals of Brownian motion (with M. Bou´e), Annals of Probability, 26 (1998), pp. 1641—1659.

Rates of convergence for approximations schemes in optimal control (with M. James), SIAM J. on Control and Opt. 36 (1998), pp. 719—741.

Risk sensitive and robust escape criteria (with W. McEneany), SIAM J. on Control and Opt. 35 (1997), pp. 2021—2048.

A Weak Convergence Approach to the Theory of Large Deviations (with R. S. Ellis), John Wiley & Sons, New York, 1997.

A nonstandard form of the rate function for the occupation measure of a Markov chain (with O. Zeitouni), Stoch. Proc. and Their Appl., 61 (1996),pp. 249—261.

The large deviation principle for a general class of queueing systems, I (with R. S. Ellis), Transactions of the AMS 347 (1995), pp. 2689—2751.

A dynamical systems approach for network oligopolies and variational inequalities, (with A. Nagurney and D. Zhang), Annals of Regional Science 28 (1994), pp. 263—283.

An optimal control formulation and related numerical methods for a problem in shape reconstruction, (with J. Oliensis), The Annals of Applied Probability 4 (1994), pp. 287—346.

Lyapunov functions for semimartingale reflecting Brownian motions, (with R. J. Williams), The Annals of Probability 22 (1994), pp. 680—702.

Dynamical systems and variational inequalities, (with A. Nagurney), The Annals of Operations Research 44 (1993), pp. 9—42.

SDEs with oblique reflections on nonsmooth domains, (with H. Ishii), The Annals of Probability 21 (1993), pp. 554—580.

Large deviations for Markov processes with discontinuous statistics, II: Random walks, (with R. S. Ellis), P robability Theory and Related Fields 91 (1992), pp. 153—194.

On sampling-controlled stochastic approximation, (with R. Simha), IEEE Trans. on Auto. Control 35 (1991), pp. 915—925.

Large deviations for Markov processes with discontinuous statistics, I: general upper bounds, (with R. S. Ellis and A.Weiss), The Annals of Probability 19 (1991), pp. 1280—1297.

On Lipschitz continuity of the solution mapping to the Skorokhod Problem, with applications, (with H. Ishii), Stochastics 35 (1991), pp. 31—62.

On oblique derivative problems for fully nonlinear second-order elliptic PDE's on domains with corners, (with H. Ishii), Hokkiado U. Math. J. 20 (1991), pp. 135—164.

On oblique derivative problems for fully nonlinear second-order elliptic PDE's on nonsmooth domains, (with H. Ishii), J. of Nonlinear Analysis: Theory, Methods and Applications 15 (1990), pp. 1123—1138.

A viscosity solution approach to the asymptotic analysis of queueing systems, (with H. Ishii and H. M. Soner), The Annals of Probability 18 (1990), pp. 226—255.

Minimizing exit probabilities; a large deviations approach (with H. J. Kushner), SIAM J. on Control and Optimization. 27 (1989), pp. 432—445.

Stochastic approximation and large deviations: upper bounds and w.p.1 convergence, (with H. J. Kushner), SIAM J. on Control and Optimization., 27 (1989), pp. 1108—1135.

Large deviations analysis of some recursive algorithms with state dependent noise, The Annals of Probability 16 (1988), pp. 1509—1536.

Large deviations analysis of reflected diffusions and constrained stochastic approximation algorithms in convex sets, Stochastics 21 (1987), pp. 63—96.

Stochastic systems with small noise, analysis and simulation; a phase locked loop example (with H. J. Kushner), SIAM J. on Applied Math. 47 (1987), pp. 643—661.

Asymptotic theory of constrained stochastic approximations via the theory of large deviations (with H. J. Kushner), Probability Theory and Related Fields 75 (1987), pp. 223—244.

Large deviations estimates for systems with small noise effects, and applications to stochastic systems theory (with H. J. Kushner), SIAM J. on Control and Optimization 24 (1986), pp. 979—1008.

Stochastic approximation via large deviations: asymptotic properties (with H. J. Kushner), SIAM J. on Control and Optimization 23 (1985), pp. 675—696.

Dynamic importance sampling for queueing networks (with D. Sezer and H.Wang), submitted to Annals of Appl. Probab.

Subsolutions of an Isaacs equation and efficient schemes for importance sampling: Convergence analysis (with H. Wang), submitted to Math. of OR.

Refined large deviation asymptotics for the classical occupancy problem (with J. Zhang and P.Whiting), submitted to Method. and Comp. in Applied Probab.

Large deviation principle for occupancy problems with colored balls (with Carl Nuzman and Phil Whiting), submitted to Adv. Applied Probability.

Large deviation principle for general occupancy models (with J. Zhang), submitted to Combinatorics, Probability and Computing.

Subsolutions of an Isaacs equation and efficient schemes for importance sampling: Examples and numerics (with H. Wang), submitted to Math. of OR.

research overview

My main interests are in applications of probability and in the control of deterministic and stochastic processes. Tools used are large deviation theory, which explains how rare events occur in random processes, numerical methods such as Markov chain approximations and Monte Carlo simulation, and partial differential equations.

research statement

Please see curriculum vita

funded research

Current Funding: Army Research Office and National Science Foundation