Research

Research Interests

I work on stochastic analysis and probabilistic aspects of fluid dynamics and the Boltzmann equation. Ergodic  behavior, perturbation by fractional Brownian noise,  backward stochastic equations, systems with Markov switching, and  large deviations principle form a list of problems that I have studied in the context of stochastic Navier-Stokes and related equations. Constructions of Boltzmann processes and the Boltzmann-Enskog process,  and investigation of their uniqueness, stability and regularity form part of my current work. My research is based on  semimartingale theory,  stochastic differential (and partial) differential equations, martingale  problems, interacting particle systems, ergodic theory, and the large deviations principle. 

Publications

Books

• Stochastic Analysis and Diffusion Processes  by Gopinath Kallianpur and P. Sundar, Oxford Graduate Texts in Mathematics 24,  2014. 

• Infinite Dimensional Stochastic Analysis: In Honor of Hui-Hsiung Kuo Ed. by Ambar  Sengupta and P. Sundar, World Scientific, 2007.

Publications

1. (with Po-Han Hsu) Ergodicity for three-dimensional stochastic Navier-Stokes equations with Markovian switching;  Stochastic Anal. and Appl., 42, 264-287, 2024.

2. (with H.-H. Kuo, Pujan Shrestha, Sudip Sinha) On Near-martingales and a class of anticipating linear stochastic differential equations; Infinite-dimensional analysis, Quantum Probability and Related Topics, published online, Dec. 2023.

3. (with Po-Han Hsu) Three-Dimensional stochastic Navier-Stokes equations with Markov switching; Stochastics and Dynamics, 23, No. 7, 2023  (41 pages).

4. (with S. Albeverio, B. Rüdiger) On the construction and identifcation of Boltzmann processes; Ensaios Mathemáticos, 38, 1-22, Papers in honor of Errico Presutti, Sociedade Brasileira de Mathematica , 2023.

5. (with M. Friesen, B. Rüdiger) On uniqueness and stability for the Boltzmann-Enskog equation; Nonlinear Differential Equations and Applications, 29, Art. no: 25, 2022.

6. (with A. Ganguly) Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics; Stochastic Processes and their Applications, 133, 74-110, 2021.

7. (with M. Friesen, B. Rüdiger) The Enskog process for hard and soft potentials; Nonlinear Differential Equations and Applications, 26, Art. no. 20 (42 pages), 2019.

8. (with Po-Han Hsu) Exponential inequalities for exit times for stochastic Navier-Stokes equations and a class of evolutions; Communications on Stochastic  Analysis,12, 343-358, 2018.

9. Book Review: Yosida approximations of stochastic differential equations in infinite dimensions and applications, Bulletin of AMS, 55, no. 2, 315-319, 2018.

10. (with S. Albeverio, B. Rüdiger) The Enskog Process;  Journal of Statistical Physics, 167, 90-122, 2017 (with S. Albeverio, B. Rüdiger)

11.  (with H. Leiva) Approximate controllability of the Burgers equation with impulses and delays; Far East Journal of Math. Sci., 102, 2291-2306, 2017.

12. (with H. Leiva) Existence of solutions for a class of semilinear evolution equations with impulses and delays;  Journal of Nonlinear Evolution equations and Applications, 7, 95-108, 2017.

13. (with L. Fang and F. Viens) Two-dimensional stochastic Navier-Stokes equations with fractional Brownian noise;  Random Operators and Stochastic Equations, 21, 135 - 158, 2013. 

14. (with Kalyan Raman) Towards a Resolution of the Reference Pressure Controversy in Cerebrospinal Fluid Flow Dynamics;  Cerebrospinal Fluid: Functions, Composition and Disorders, Ed. V. Slavik and T. Dolezal, Nova Science Publishers, 107-121, 2012. 

15. (with Ming Tao)  A Representation for Positive Functionals of a Brownian Motion and an Application,  Communications on Stochastic Analysis, 6, 669-687, 2012. 

16. Stochastic MHD System perturbed by a general noise;  Communications on Stochastic Analysis, 4, 253-269, 2010. 

17. (with U. Manna and S.S. Sritharan) Large deviations for the stochastic shell model of turbulence ; Nonlinear Differential Equations and Applications,16, 493-521, 2009. 

18. (with Hong Yin) Existence and Uniqueness of Solutions to the Backward 2D Stochastic Navier-Stokes Equations;  Stochastic Processes and their Appl., 119, 1216-1234, 2009. 

19. (with Hong Yin) Adapted Solutions to the Backward Stochastic Navier-Stokes Equations in 3D;  Infinite Dimensional Stochastic Analysis: In Honor of H.-H. Kuo ,World Scientific, 114-134, 2008. 

20. (with Hong Yin)  Existence and Uniqueness of Solutions to the Backward Stochastic Lorenz System ; Comm. on Stoch. Analysis, 1, no. 3, 473-483, 2007. 

21.  (with S.S. Sritharan) Large Deviations for the Two-Dimensional Navier-Stokes Equations with Multiplicative Noise ; Stochastic Processes and their Appl., 116, 1636-1659, 2006. 

22.  A note on the solution of a stochastic partial differential equation; Stochastic Analysis and Appl., 22, 923-938, 2004.

23.  (with T. Koski) Two applications of reproducing kernel Hilbert spaces in stochastic analysis;  Stochastics in Finite and Infinite Dimensions: In Honor of G. Kallianpur, ed. T. Hida et al., Trends in Mathematics Series, Birkhauser, 195-206, 2001. 

24.  (with G. Ferreyra) Comparison of solutions of stochastic equations and applications;  Stochastic Anal. Appl., 18, 211-229, 2000. 

25.  (with S.S. Sritharan)  Ergodic Control of Stochastic Navier-Stokes Equation;  Nonlinear problems in Aviation and Aerospace, ed. S. Sivasundaram, Gordon Breach Publications, 213-221, 2000. 

26.  (with G. Kallianpur) Hilbert Space Valued Super Brownian Motion and Related Evolution Equations; J. of Appl. Math. and Optim.,  41, 111-128, 2000. 

27.  (with G. Ferreyra) Comparison of stochastic Volterra equations;  Bernoulli, 6, 1001-1006, 2000.

28.  (with A. Bose) Weak convergence of systems of interacting SDEs to the superprocess;  J. of Appl. Math. and Optim.,  41, 141-154, 2000. 

29. (with J. R. Dorroh and G. Ferreyra) A technique for stochastic control problems with unbounded control set;  Journal of Theoretical Probability, 12, No. 1, (1999) 255-270.

30. (with G. Ferreyra) Pathwise Comparison of Arithmetric Brownian Motions and Log-normal Processes;  Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming}, Systems \& Control: Foundations \& Applications series,Birkh\"{a}user, Boston, 1999, 541-546.

31. (with S. S. Sritharan) The Stochastic magneto-hydrodynamic system; Infinite Dimensional Analysis, Quantum Probability, and Related Topics,  2, No. 2, (1999) 241 - 265.

32. (with T. Koski) Expansion of filtrations and Gaussian semimartingales;  Journal of Combinatorics, Information and System Sciences, 22, nos. 3-4 (1997), 203-224.

33. (with J. R. Dorroh and G. Ferreyra) Stochastic control problems with unbounded control set;  Proceedings of the IEEE SoutheastConf'96 (1996) 128-131.

34. (with J. Potthoff) Law of large numbers and central limit theorem for Donsker's delta function of diffusions I;  J. Potential Analysis, 5 (1996) 487-504. 

35. (with J. R. Dorroh and G. Ferreyra) Diffusions with unbounded controls; Proceedings of the 33th IEEE Conference on Decision and Control, (1994) 2591-2593.

36. (with J. Potthoff) Limits for the Donsker delta function: An example; Stochastic Analysis and Related Topics, Ed. Lindstrom, Oksendal, Ustunel,  North Holland Stochastic Monograph Series, 8 (1994) 217-227.  

37. (with J. Potthoff) Law of large numbers and central limit 

38. (with J. Potthoff) Law of large numbers and central limit theorem for Donsker's delta function; Stochastics and Stochastic Reports, 42 (1993) 135-150.

39. (with T.S. Chiang and G. Kallianpur) Propagation of chaos for systems of interacting neurons; Pitman Research Notes in Mathematics, 268 (1991) 98-110.

40. (with T.S. Chiang and G. Kallianpur) Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces;  J. App. Math. and Optim., 24 (1991) 55-83.

41. Time reversal of solutions of equations driven by L\'evy processes; Diffusion proc. and rel. problems in Anal. 2 (1991) 110-120, Birkhauser, Boston.

42. Ergodic solutions of stochastic differential equations; Stoch. and Stoch. Reports,  28 (1989) 65-83.

43. Comparison between solutions of SDEs and ODEs;  Stoch. Proc. and their Appl.,  30 (1988) 165-169.

44. Law of the iterated logarithm for solutions of stochastic differential equations; Stoch. Anal. and Appl.  5 (1987) 311-321.