**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.

**Book**

A. Budhiraja and P. Dupuis. *Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods*, Probability Theory and Stochastic Modelling, Volume 94, Springer, 2019. (Errata)

**Publications and Preprints**

*Arranged in reverse chronological order*

Diffusion limits in the quarter plane and non-semimartingale reflected Brownian motion, with R. Atar. *Submitted*.

**Ergodic Control of Resource Sharing Networks: Lower Bound on Asymptotic Costs**, with M.Conroy and D.Johnson. *Under Review.*

**Fluctuations of the Atlas model from inhomogeneous stationary profiles,** with S. Banerjee and P. Rudzis. *Under Review.*

**Large Deviations for Empirical Measures of Self-Interacting Markov Chains**, with A. Waterbury and P. Zoubouloglou. *Under Review*.

**Long Time Behavior of Finite and Infinite Dimensional Reflected Brownian Motions**, with S. Banerjee. Book Chapter in *Probability and Stochastic Processes*, Springer, 2024.

**Extremal Invariant Distributions of Infinite Brownian Particle Systems with Rank Dependent Drifts**, with S. Banerjee. *Under Review.*

**Large Deviations for Small Noise Diffusions Over Long Time**, with P. Zoubouloglou. *Transactions of the American Mathematical Society*, Series B. 2024;11(01):1-63.

**Simple Form Control Policies for Resource Sharing Networks with HGI Performance**, with D. Johnson. *The Annals of Applied Probability*, 2024 Feb;34(1B):851-916.

**Load Balancing in Parallel Queues and Rank-based Diffusions**, with S. Banerjee and B. Estevez. *Math. Oper. Res.*, to appear, 2024.

On Some Extensions of the Boué-Dupuis Variational Formula, Submitted, 2024.

**Large deviation principles for functionals of fractional Brownian motions,** with X. Song. *IISA Volume on Statistics and Data Science, to appear*, 2024.

**The Inert Drift Atlas Model,** with S. Banerjee and B. Estevez. *Communications in Mathematical Physics*, 2023 May;399(3):2083-147.

**Empirical Measure Large Deviations for Reinforced Chains on Finite Spaces**, with A. Waterbury. *Systems and Control Letters*, 2022; 169, 105379.

**Domains of attraction of invariant distributions of the infinite Atlas model****,** with S. Banerjee. *The Annals of Probability*, 2022 Jul; 50(4):1610-46.

**Quasistationary Distributions and Ergodic Control Problems****,** with P. Dupuis, P. Nyquist, G-J. Wu. *Stochastic Processes and their Applications*, 2022 Mar 1;145:143-64..

**Approximating Quasi-Stationary Distributions with Interacting Reinforced Random Walks, **with N. Fraiman, A. Waterbury. *ESAIM: Probability and Statistics*, 2022;26:69-125.

**Asymptotic Behavior of Stochastic Currents under Large Deviation Scaling with Mean Field Interaction and Vanishing Noise****,** with M. Conroy. * Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, to appear.*

**Near Equilibrium Fluctuations for Supermarket Models with Growing Choices**, with S. Bhamidi and M. Dewaskar. *Annals of Applied Probability, *2022 Jun;32(3):2083-138*.*

**Empirical Measure and Small Noise Asymptotics under Large Deviation Scaling for Interacting Diffusions**, with M. Conroy. *J. Theor. Prob*., 2021, pages 1-55.

**Many-Server Asymptotics for Join-the-Shortest-Queue: Large Deviations and Rare Events**, with E. Friedlander and R.Wu. *Ann. App. Prob.*,2021 Oct; 31(5):2376-419.

**Large Deviations for the Single Server Queue and the Reneging Paradox**, with R. Atar, P. Dupuis, R. Wu. *Math. Oper. Res*., 2022 Feb;47(1):232-58.

**Minimization of a Class of Rare Event Probabilities and Buffer Probabilities of Exceedance**, with S. Lu, Y. Yu, Q. Tran-Dinh. *Ann. Oper. Res*., 2021 Jul; 302(1):49-83.

https://doi.org/10.1007/s10479-021-03991-8.

**Heavy Traffic Scaling Limits for shortest remaining processing time queues with heavy tailed processing time distributions**, with S. Banerjee and A. L. Puha. *Annals of Applied Probability, to appear*.

**Robust Bounds and Optimization at the Large Deviations Scale for Queueing Models via Rényi Divergence’**, with R. Atar, P. Dupuis and R. Wu. *Ann. App. Prob.*, 2021, Vol. 31, No. 3, 1061–1099.

**Asymptotics of Quasi-Stationary Distributions of Small Noise Stochastic Dynamical Systems in Unbounded Domains**, with A. Waterbury and N. Fraiman. *Advances in Applied Probability,* 2022 Mar;54(1):64-110.

**Large Deviations of the Entropy Production Rate for a Class of Gaussian Processes,** with Y. Chen and L. Xu. *J. Math. Phys.* **62**, 052702 (2021); https://doi.org/10.1063/5.0023030.

**A new Approach to Large Deviations for the Ginzburg-Landau Model** ( with S. Banerjee and M. Perlmutter). *Elec. J. Probability*, **25**, 2020, paper no. 26, 51 pp.

**Parameter and dimension dependence of convergence rates to stationarity for Reflecting Brownian Motions,** with S. Banerjee, *Ann. App. Prob.*, 30(5), 2020, 2005-29.

**Uniform large deviation principles for Banach space valued stochastic differential equations **(with P. Dupuis and M. Salins). *Trans. Amer. Math. Soc.*, **372**, 2019, 8363–8421.

**Control Policies Approaching HGI Performance in Heavy Traffic for Resource Sharing Networks **(with Dane Johnson). *Math. Oper. Res.*, 45 (3), 2020, 797-832.

**Supermarket Model on Graphs** (with D. Mukherjee and R. Wu). *Ann. App. Prob*., **29**(3), 2019, 1740–1777.

**Diffusion Approximations for Load Balancing Mechanisms in Cloud Storage Systems** (with E. Friedlander). *Advances in Applied Probability*, **51**(1), 2019, 41-86.

**Large Deviations for Small Noise Diffusions in a Fast Markovian Environment** (with P. Dupuis and A. Ganguly). *Elec. J. Prob*., paper no. **112**, 23, 2018, 33 pp..

**Rare Event Asymptotics for Exploration Processes for Random Graphs (**with S. Bhamidi, P. Dupuis and R. Wu). *Annals of Applied Probability*, 2022 Apr; 32(2):1112-78..

**A Numerical Scheme for a Mean Field Game in Some Queueing Systems Based on Markov Chain Approximation Method **(with E. Bayraktar and A. Cohen). *SIAM J. Control Optim*., **56**(6), 2018, 4017–4044.

**Large Deviations for Brownian Particle Systems with Killing** (with W-T. Fan and R. Wu). *Journal of Theoretical Probability,* 31(3), 2018, 1779–1818.

**Rate Control under Heavy Traffic with Strategic Servers ** (with E. Bayraktar and A. Cohen). *Ann. App. Prob., ***29**(1), 2019, 1–35.

**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). *SIAM J. Appl. Math.*, **78**(5), 2018, 2279–2297.

**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)**. **S*IAM 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.** Sinica***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.