Research Interests

 

My main interests are in Probability and Stochastic Processes. Some of the topics I am interested in are Large Deviations, Stochastic Control, Stochastic Differential Games, Stochastic Networks, Stochastic Partial Differential Equations, Random Graphs, Stochastic Numerics, Nonlinear Filtering. I am a member of the probability group at UNC.

 

 

Publications and Preprints

 

Arranged in reverse chronological order

Large Deviations from the Hydrodynamic Limit for a System with Nearest Neighbor Interactions ( with S. Banerjee and M. Perlmutter). Submitted.

Uniform large deviation principles for Banach space valued stochastic differential equations (with P. Dupuis and M. Salins). Submitted.

Control Policies Approaching HGI Performance in Heavy Traffic for Resource Sharing Networks (with Dane Johnson). Submitted.

Supermarket Model on Graphs (with D. Mukherjee and R. Wu). Submitted.

Diffusion Approximations for Load Balancing Mechanisms in Cloud Storage Systems (with E. Friedlander). Submitted.

Large Deviations for Small Noise Diffusions in a Fast Markovian Environment (with P. Dupuis and A. Ganguly). Submitted.

Large Deviation Principle for the Exploration Process of the Configuration Model (with S. Bhamidi, P. Dupuis and R. Wu). Submitted.

A Numerical Scheme for a Mean Field Game in Some Queueing Systems Based on Markov Chain Approximation Method (with E. Bayraktar and A. Cohen).

Large Deviations for Brownian Particle Systems with Killing (with W-T. Fan and R. Wu). Journal of Theoretical Probability. (https://doi.org/10.1007/s10959-017-0764-2)

Rate Control under Heavy Traffic with Strategic Servers (with E. Bayraktar and A. Cohen). To appear in Ann. App. Prob.

Uniform in Time Interacting Particle Approximations for Nonlinear Equations of Patlak-Keller-Segel type (with W-T. Fan). Electron. J. Probab., 22 (2017), 37 pp.

Diffusion Approximations for Controlled Weakly Interacting Large Finite State Systems with Simultaneous Jumps (with E. Friedlander). Annals of Applied Probability, 28(1), 2018, 204–249.

Moderate Deviation Principles for Weakly Interacting Particle Systems (with R.Wu). Prob. Th. Rel. Fie., doi:10.1007/s00440-016-0723-3, 168(34), (2017), 721–771.

Source Detection Algorithms for Dynamic Contaminants Based on the Analysis of a Hydrodynamic Limit (with S. A. Almada-Monter and J. Hannig). Submitted.

Critical Random Graphs and the Differential Equations Technique (with S. Bhamidi and S. Sen). Indian Journal of Pure and Applied Mathematics., 48(4), 2017, 633–669.

Some Fluctuation Results for Weakly Interacting Multi-Type Particle Systems (with R. Wu). Stoch. Proc. App. 125(2015), no. 3, 1911–1925.

Construction of Asymptotically Optimal Control for a Stochastic Network from a Free Boundary Problem (with X.Liu and S.Saha). Stochastic Systems, 6(2), 2016, 459–518..

Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes (with P. Dupuis, M. Fischer and K. Ramanan). Elec. J. Prob. 3(2015), 1–30.

Limits of Relative Entropies Associated with Weakly Interacting Particle Systems (with P. Dupuis, M. Fischer and K. Ramanan). Elec. J. Prob. 3(2015), 1–22.

Large Deviations for Multidimensional State-Dependent Shot Noise Processes (with P. Nyquist). J. Appl. Probab. 52(2015), 1097–1114.

Individual Confidence Intervals for Solutions to Expected Value Formulations of Stochastic Variational Inequalities (with M.Lamm and S.Lu). Mathematical Programming. doi: 10.1007/s10107-016-1046-y, 165(1), 2017, 151–196.

Central Limit Results for Jump-Diffusions with Mean Field Interaction and a Common Factor (with E.Kira and S.Saha). Stochastic Analysis and Applications, 35(5), 2017, 767–802..

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). Ann. Prob., 44 (2016), no. 3, 1723–1775.

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.

On Uniform Positivity of Transition Densities of Small Noise Constrained Diffusions (with Z.Q. Chen). Electronic Communications in Probability 19 (2014), no. 1, 1-9.

The Augmented Multiplicative Coalescent and Critical Dynamic Random Graph Models (with S.Bhamidi and X. Wang). Probability Theory and Related Fields 160(2014), 733-796.

Bounded-Size Rules: The Barely Subcritical Regime (with S.Bhamidi and X. Wang). Combinatorics, Probability and Computing 23(2014), no. 4, 505-538.

Scheduling Control for Markov Modulated Single-server Multiclass Queueing Systems in Heavy Traffic (with A. Ghosh and X. Liu). Queuing Systems 78(2014), 57-97.

Admission Control for Multidimensional Workload with Heavy Tails and Fractional Ornstein-Uhlenbeck Process (with V. Pipiras and X. Song). Advances in Applied Probability. 47(2015), no. 2 (2015), 476-505.

Infinite Dimensional Forward-Backward Stochastic Differential Equations and the KPZ Equation (with S. Almada). Electronic J. Probab. 19(2014), no. 40, 1-21.

Large Deviations for Stochastic Partial Differential Equations Driven by a Poisson Random Measure (with Jiang Chen and Paul Dupuis). Stoch. Proc. App. 123 (2013), no. 2, 523-560.

Near Critical Catalyst Reactant Branching Processes with Controlled Immigration (with Dominik Reinhold). Ann. App. Prob. 23 (2013), no. 5, 2053-2098.

Confidence Regions for Stochastic Variational Inequalities (with Shu Lu). Math. Oper. Res. 38 (2013), no. 3, 545-568.

A Numerical Scheme for Invariant Distributions of Constrained Diffusions (with Jiang Chen and Sylvain Rubenthaler). Math. Oper. Res. 39(2014), no. 2, 262-289.

Aggregation models with limited choice and the multiplicative coalescent(with Shankar Bhamidi and Xuan Wang). Random Structures and Algorithms 46(2015), no. 1, 55-116.

Discrete Time Markovian Agents Interacting Through a Potential (with Pierre Del Moral and Sylvain Rubenthaler). ESAIM: Prob. and Stat. 17 (2013), 614-634.

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.

Ergodic Rate Control Problem for Single Class Queueing Networks (with Arka Ghosh and Chihoon Lee). SIAM J. Cont. Opt. 49 (2011), no. 4, 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. 34 (2009), no. 1, 45-56.

Optimal Stopping and Free Boundary Characterizations for some Brownian Control Problems (with Kevin Ross) Ann. App. Prob. 18 (2008), no. 6, 2367-2391.

Large Deviations for Infinite Dimensional Stochastic Dynamical Systems (with Paul Dupuis and Vasileios Maroulas). Ann. Prob. 36 (2008), no. 4, 1390-1420.

Modified Particle Filter Methods for Assimilating Lagrangian Data into a Point-Vortex Model (with E.T. Spiller, K. Ide and C. Jones). Phys. D 237 (2008), no. 10-12, 1498–1506.

Deterministic and Stochastic Differential Inclusions with Multiple Surfaces of Discontinuity (with Rami Atar and Kavita Ramanan). Probability Theory and Related Fields, 142 (2008), no. 1-2, 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.

A survey of numerical methods for nonlinear filtering problems. (with Chihoon Lee). Phys. D 230 (2007), no. 1-2, 27–36.

Existence of Optimal Controls for Singular Control Problems with State Constraints (with Kevin Ross). Ann. App. Prob. 16(2006), no.4, 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, 59–87, Trends Math., 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 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. 59, (1999), 1686-1700.

Approximation and Limit Results for Nonlinear Filters Over an Infinite Time Interval(with H. Kushner)SIAM J. Cont. Opt. 37, No. 6, (1999), 1946-1979.

Robustness of Nonlinear Filters Over the Infinite Time Interval (with H. Kushner). SIAM J. Control and Opt. 36, (1998), 1618-1637.

A Limit Theorem for Symmetric Statistics of Brownian Particles Stochastic Processes and their Applications 77, (1998), 155-174.

Exponential Stability of Discrete-Time Filters for Bounded Observation Noise (with D. Ocone). System and Control Letters 30, (1997) 185-193.

Approximations to Solutions of Zakai Equations Using Multiple Wiener and Stratonovich Expansions (with G. Kallianpur).  Stochastics and Stochastic Reports 3, (1996), 271-315.

Hilbert Space Valued Traces and Multiple Stratonovich Integrals with Statistical Applications.(with G. Kallianpur). Probability and Mathematical Statistics 15, (1995), 127-163.

The Feynman-Stratonovich Semigroup and Stratonovich Integral Expansions in Nonlinear Filtering (with G. Kallianpur). Appl. Math. Optim.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. Sinica7 (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.