Some Fluctuation Results for Weakly Interacting Multi-type Particle Systems (with R.Wu). Submitted.
Construction of Asymptotically Optimal Control for a Stochastic Network from a Free Boundary Problem (with X.Liu and S.Saha). Submitted.
Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes (with P. Dupuis, M. Fischer and K. Ramanan). Submitted.
Limits of relative entropies associated with weakly interacting particle systems (with P. Dupuis, M. Fischer and K. Ramanan). Submitted.
Large deviations for multidimensional state-dependent shot noise processes (with P. Nyquist). To Appear in Adv. App. Prob.
Individual confidence intervals for true solutions to stochastic variational inequalities (with M.Lamm and S.Lu). Submitted.
On the multi-dimensional skew Brownian motion (with R. Atar). Stoch. Proc. App., 125(2015), no. 3, 1911–1925.
Moderate deviation principles for stochastic differential equations with jumps (with P. Dupuis and A. Ganguly). To Appear in Ann. Prob..
Long time results for a weakly interacting particle system in discrete time (with A. Pal Majumdar). Stoch. Anal. App, 33 (2015), no. 3, 429-463 .
Stability of Constrained Markov Modulated Diffusions (with Xin Liu). Math. Oper. Res. 37 (2012), no. 4, 626–653.
Controlled Stochastic Networks in Heavy Traffic: Convergence of Value Functions (with Arka Ghosh). Ann. App. Prob., 22 (2012), Number 2, 734-791.
Exit Time and Invariant Measure Asymptotics for Small Noise Constrained Diffusions (with Anup Biswas). Stoch. Proc. App. 121(2011), 899 -- 924.
Action Time Sharing Policies for Ergodic Control of Markov Chains (with Adam Shwartz and Xin Liu). SIAM J. Control Optim., 50, (2012), no. 1, 171-195.
Multiscale Diffusion Approximations for Stochastic Networks in Heavy Traffic (with Xin Liu). Stoch. Proc. App. 121(2011), 630 --656.
Large deviation properties of weakly interacting processes via weak convergence methods (with Paul Dupuis and Markus Fischer). Ann. Prob., 40 (2012), no. 1, 74-102.
Some asymptotic results for near critical branching processes (with Dominik Reinhold). Comm. on Stoch. Anal. 4 (2010), no. 1, 91—113.
Variational Representations for Continuous Time Processes (with P. Dupuis and V. Maroulas). Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, 47 (2011), no. 3, 725 -- 747.
On Near Optimal Trajectories of Games Associated with the infinity-Laplacian (with Rami Atar). Prob. Th. Rel Fiel., 151 (2011), no. 3-4, 509–528.
A stochastic differential game for the inhomogeneous infinity-Laplace equation (with Rami Atar). Ann. Prob. 38 (2010), no. 2, 498—531.
An Ergodic Rate Control Problem for Single Class Queueing Networks (with Arka Ghosh and Chihoon Lee). SIAM J. Cont. Opt., 49, no. 4 (2011), 1570–1606.
Large Deviations for Stochastic Flows of Diffeomorphisms (with P. Dupuis and V. Maroulas). Bernoulli 16 (2010), no. 1, 91--113.
Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic (with Chihoon Lee). Math. Oper. Res., Vol. 34, No. 1, February 2009, pp. 45-56.
Optimal Stopping and Free Boundary Characterizations for some Brownian Control Problems (with Kevin Ross) Ann. App. Prob., 18, no. 6, 2367-2391.
Large Deviations for Infinite Dimensional Stochastic Dynamical Systems (with Paul Dupuis and Vasileios Maroulas). Ann. Prob., 36, no. 4 (2008), 1390-1420.
Deterministic and Stochastic Differential Inclusions with Multiple Surfaces of Discontinuity (with Rami Atar and Kavita Ramanan). Probability Theory and Related Fields, 142, no. 1-2 (2008), 249-283.
HJB Equations for Certain Singularly Controlled Diffusions (with Rami Atar and Ruth J. Williams). Ann. App. Prob., 17 (2007), no. 5-6, 1745-1776.
Long time asymptotics for constrained diffusions in polyhedral domains (with Chihoon Lee). Stochastic Processes and their Applications 117 (2007) 1014-1036.
Existence of Optimal Controls for Singular Control Problems with State Constraints (with Kevin Ross). Ann. App. Prob., 16, no. 4(2006), 2235-2255.
Convergent Numerical Scheme for Singular Stochastic Control with State Constraints in a Portfolio Selection Problem (with Kevin Ross). SIAM J. Cont. Opt., 45 (2007), no. 6, 2169-2206.
Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function (with Arka Ghosh). Ann. App. Prob., 16, no. 4 (2006), 1962-2006.
Molecular Motors, Brownian Ratchets, and Reflected Diffusions (with John Fricks). Discrete and Continuous Dynamical Systems, Series B, 6 , no. 4 (2006), 711-734.
Singular Control with State Constraints on Unbounded Domain (with Rami Atar). Ann. Prob., 34, no. 5 (2006), 1864-1909.
A Large Deviations Approach to Asymptotically Optimal Control of Crisscross Network in Heavy Traffic (with A. P. Ghosh). Ann. App. Prob. 15 (2005), no. 3, 1887-1935.
Ergodic Control for Constrained Diffusions: Characterization using HJB Equations (with V. Borkar). SIAM J. Control Optim. 43 (2004/05), no. 4, 1467-1492.
A Further Remark on Dynamic Programming For Partially Observed Markov Processes (with V. Borkar) Stochastic Processes and their applications, 112 (2004), no. 1, 79-93.
Stochastic Differential Equation for TCP Window Size: Analysis and Experimental Validation (with F. Hernandez-Campos, V.G. Kulkarni and F.D. Smith) Probability in the Engineering and Informational Sciences, 18 (2004), 111-140.
Asymptotic Stability, Ergodicity and other asymptotic properties of the Nonlinear Filter Annales de l'Institut Henri Poincare: Probabilites et statistiques, 39 (2003), no. 6, 919-941.
Stability Properties of Constrained Jump-Diffusion Processes (with R. Atar) Electron. J. Probab. 7 (2002), no. 22, 31 pp. (electronic).
Large Deviations for the Empirical Measures of Reflecting Brownian Motion and Related Constrained Processes in R+ (with P. Dupuis) Electron. J. Probab. 8 (2003), no. 16, 46 pp. (electronic).
An Ergodic Control Problem for Constrained Diffusion Processes: Existence of Optimal Markov Control. SIAM J. Control Optim. 42 (2003), no. 2, 532-558.
On Positive Recurrence of Constrained Diffusion Processes (with R. Atar and P. Dupuis) Annals of Probability, 29 (2001), no. 2, 979-1000.
On invariant measures of discrete time filters in the correlated signal-noise case. Ann . Appl. Prob. 12 (2002), no. 3, 1096-1113.
Ergodic properties of the nonlinear filter. Stochastic Processes and their applications, 95 (2001) 1-24.
A variational representation for positive functionals of an infinite dimensional Brownian motion (with P.Dupuis). Probab. Math. Statist. 20 (2000), no. 1, 39-61.
Markov Property and Ergodicity of the Nonlinear Filter (with A.G. Bhatt and R.L.Karandikar). SIAM J. Control Optim. 39 (2000), no. 3, 928-949.
Monte Carlo Algorithms and Asymptotic Problems in Nonlinear Filtering (with H.J. Kushner). Stochastics in finite and infinite dimensions, A volume in honor of G. Kallianpur.
A nonlinear filtering algorithm based on an approximation of the conditional distribution (with H.J. Kushner). IEEE Trans. Automat. Control 45 (2000), no. 3, 580-585.
Exponential stability in discrete time filtering for non-ergodic signals (with D.Ocone). Stochastic Processes and their applications, Vol. 82, (1999), 245-257.
Approximation and limit results for nonlinear filters over an infinite time interval: Part II, random sampling algorithms (with H. Kushner). SIAM J. Control Optim. 38 (2000), no. 6, 1874-1908.
Representations for functionals of Hilbert space valued diffusions (with P. Dupuis). Stochastic analysis, control, optimization and applications, 1-20, Systems Control Found. Appl., Birkhäuser Boston, Boston, MA, 1999.
Simple necessary and sufficient conditions for the stability of constrained processes (with P. Dupuis). SIAM J. Appl. Math., Vol. 59, (1999), 1686-1700.
Approximation and limit results for nonlinear filters over an infinite time interval (with H. Kushner). SIAM J. Cont. Opt., Vol. 37, No. 6, (1999), 1946-1979.
Robustness of nonlinear filters over the infinite time interval (with H. Kushner). SIAM J. Control and Opt. Vol. 36, (1998), 1618-1637.
A limit theorem for symmetric statistics of Brownian particles. Stochastic Processes and their Applications, Vol. 77, (1998), 155-174.
Exponential stability of discrete time filters for bounded observation noise (with D. Ocone). System and Control Letters, Vol. 30, (1997) 185-193.
Approximations to solutions of Zakai equations using multiple Wiener and Stratonovich expansions (with G. Kallianpur). Stochastics and Stochastic Reports, Vol. 3, (1996), 271-315.
Hilbert space valued traces and multiple Stratonovich integrals with statistical applications (with G. Kallianpur). Probability and Mathematical Statistics, Vol. 15, (1995), 127-163.
The Feynman-Stratonovich semigroup and Stratonovich integral expansions in nonlinear filtering (with G. Kallianpur). Appl. Math. Optim. Vol. 35, (1997), no. 1, 91-116.
The generalized Hu-Meyer formula for random kernels (with G. Kallianpur). Appl. Math. Optim. 35 (1997), no. 2, 177-202.
Two results on multiple Stratonovich integrals (with G. Kallianpur). Statist. Sinica Vol. 7 (1997), no. 4, 907-922.
Hilbert space valued traces and multiple Stratonovich integrals with statistical applications (with G. Kallianpur). Stochastic analysis on infinite-dimensional spaces (Baton Rouge, LA, 1994), 26--32, Pitman Res. Notes Math. Ser., 310, Longman Sci. Tech., Harlow, 1994.
May 14, 2015