My main interests are in stochastic partial differential equations (SPDEs) and their applications. As its name suggests, SPDEs is an interdisciplinary area at the crossroads of stochastic processes and partial differential equations. In recent years, my research has focused on the development of spectral methods, in particular, the Wiener Chaos expansions for SPDEs. Applications of SPDEs to fluid dynamics in turbulent flows and nonlinear filtering (Hidden Markov Models) for spatial-temporal processes are the applications of SPDEs I am most interested in.

Please visit my webpages at https://www.brown.edu/academics/applied-mathematics/boris-rozovsky

Please visit my webpages at https://www.brown.edu/academics/applied-mathematics/boris-rozovsky

R. Mikulevicius and B. Rozovsky and , “On distribution free Skorokhod- Malliavin Calculus”, J. Stochastic Partial Differential Equations: Analysis and Computations, 2016

 

Z. Zhang, B. Rozovsky, and G. E. Karniadakis. “Strong and weak convergence rate of finite element methods for semi-linear equations with additive white noise” J. of  Numer. Math.,134: 61-89, 2016

 

Z. Zhang, M. V. Tretyakov, B. Rozovskii, and G. E. Karniadakis. “Wiener chaos vs stochastic collocation methods for linear advection-diffusion quations with multiplicative white noise”. SIAM J. Numer. Anal., 53(1): 153-183, 2015

 

Zhang, M. V. Tretyakov, B. Rozovsky, and G. E. Karniadakis. “A recursive sparse grid collocation method for differential equations with white noise”. SIAM J. Sci. Comput., 36(4): pp. A1652–A1677, 2014.

 

D. Venturi, X. Wan, R. Mikulevicius, B. L. Rozovsky, G. E. Karniadakis,  “Wick-Malliavin approximations to nonlinear stochastic partial differential equations: analysis and simulations”. Proceedings of the Royal Society, 2013

 

S. Lototsky, B. Rozovsky, and D. Selesi. “On Generalized Malliavin Calculus”. Stochastic Analyses and Applications, 122, pp 808-843, 2012.

 

R. Mikulevicius and B. Rozovsky, “On unbiased stochastic Navier-Stokes equation”, Probab. Theory Related Fields, 154, pp. 787-834, 2012.

 

Lototsky, B. Rozovsky, and D. Selesi. “On Generalized Malliavin Calculus”, Stochastic Analyses and Applications, 122, pp 808-843, 2012.

 

R. Mikulevicius and B. Rozovsky, “On unbiased stochastic Navier-Stokes equation”, Probab. Theory Related Fields, 154, pp. 787-834, 2012.

 

Zhang, B. Rozovsky, M.V. Tretyakov and G.E. Karniadakis, “A multi-stage Wiener chaos expansion method for stochastic advection-diffusion –reaction equations", SIAM J. Sci. Comput., 34(2), pp. A914-A936, 2012.

 

B. Rozovsky¸ J. Park and R. Sowers, “Efficient Nonlinear Filtering of a Singularly Perturbed Stochastic Hybrid System” London Math. Society J. of Mathematics and Computation, (submitted), 2012.

 

S. Lototsky , B. Rozovsky, and X. Wan, “Elliptic equations of higher stochastic order ESAIM: Math. Modeling and Numerical Anal.”, 44 (2010) no. 5, pp. 1135-1153, 2010.

 

R. Mikulevicius and B. Rozovsky, “On unbiased stochastic Navier-Stokes equation”, Probab. Theory Related Fields, 154, pp. 787-834, 2012.

 

B. Rozovsky¸ J. Park and R. Sowers, “Efficient Nonlinear Filtering of a Singularly Perturbed Stochastic Hybrid System” London Math. Society J. of Mathematics and Computation, (submitted), 2012.

 

S. Lototsky , B. Rozovsky, and X. Wan, “Elliptic equations of higher stochastic order ESAIM: Math. Modeling and Numerical Anal.”, 44 (2010) no. 5, pp. 1135-1153, 2010.

 

Crisan, B. Rozovsky (Eds) The Oxford Handbook on Nonlinear Filtering, Oxford University Press, 2011.

 

C.-Y. Lee, B. Rozovsky, and H. M. Zhow, “ Randomization of forcing in large systems of PDE for improvement of energy estimates”, SIAM J. Multiscale Modeling and Simulation, 8, no. 4, 1419-1438, 2010.

 

X. Wan, B. Rozovsky and G.E. Karniadakis, “A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus”, Proc. Nat. Acad. Sciences, vol. 106, no. 34, pp. 14189-14194, 2009.

 

S. Lototsky , B. Rozovsky, “A unified approach to stochastic evolution equations using the Skorokhod integral”, Probability Theory and Appl., 54 , no. 2, 2009.

 

S. Lototsky , B. Rozovsky. Stochastic differential equations driven by purely spatial noise, SIAM J. on Mathematical Analysis, 41, no.4, 1295-1322, 2009.

 

Vilnius University, Doctor of Physical and Mathematical Sciences, 1984

Institute of Mathematical Statistics, Fellow, 1997

International Academy of Natural and Social Sciences, Peter-the-Great Medal, 1997

International Conference "Kolmogorov and Contemporary Mathematics",
Kolmogorov Medal, 2003

Named Ford Foundation Professor of Applied Mathematics, 2009

Journal “Stochastic Partial Differential Equations: Analysis and Computations”. Springer, (2012-present, Editor-in Chief),

SIAM J. on Uncertainty Quantification (2012-present, Associate Editor),

Bernoulli Journal (2012-present, (2012-present, Associate Editor),

Stochastic Modeling and Applied Probability, Springer-Verlag (2001-2012, Editor),

SIAM J. on Mathematical Analysis (2001-2012 , Associate Editor)

Asymptotic Analysis (2006-present, Member of Advisory Board)

Annals of Probability (1997-2002, Associate Editor )

Electronic Journal of Probability (1995-2002, Associate Editor)

Stochastic Processes and their Applications (1996-1998, Associate Editor)

American Mathematical Society

Institute of Mathematical Statistics

Society for Industrial and Applied Mathematics