At present, I work on various nonlocal PDEs using its underlying probabilistic structure. I also have interest in stochastic control.

These are some of my recent publications (For a complete list of my publications, visit Here. Some articles on ArXiv might differ a little from the published versions):

• Mixed local-nonlocal operators: maximum principles, eigenvalue problems and their applications, (w/ Mitesh Modasiya), accepted in Journal d'Analysis Math. 

• Nonlocal ergodic control problem in Rd, (w/ Erwin Topp) appeared online in Math. Annalen

• Ergodic risk-sensitive control--a survey (w/ Vivek S. Borkar) Annual Reviews in Control, Vol. 55,  118--141, 2023

• Existence-Uniqueness for nonlinear integro-differential equations with drift in Rd, (w/ Saibal Khan)  SIAM J. of Mathematical Analysis, Vol. 55, 2023 (There is a glitch in the statement of  Theorem 5.1 in the published version. For all \gamma should be read as for some \gamma. The correct statement appears in the latest arXived version)

• On the monotonicity property of the generalized eigenvalue for weakly-coupled cooperative elliptic system, (w/ Ari Arapostathis, Somnath Pradhan) Journal of Differential Equations, Vol 351, 156–193, 2023

• Generalized principal eigenvalues on Rd of second order elliptic operators with rough nonlocal kernel, (w/ Ari Arapostathis, Prasun Roychowdhury) Nonlinear Differential Equations and Applications 30, No. 10, 2023

• Boundary regularity of mixed local-nonlocal operators and its application, (w/ Mitesh Modasiya, Abhrojyoti Sen) Annali di Matematica Pura ed Applicata 202, 679-710, 2023

• Harnack inequality and principal eigentheory for general  infinity Laplacian  operators with gradient in RN and applications (w/ Hoang-Hung Vo)  CVPDE 61, Article number: 122 (2022)

• Ergodic Risk-Sensitive Control of Markov Processes on Countable State Space Revisited, (w/ Somnath Pradhan) ESAIM COCV 28 (2022)

• On ergodic control problem for viscous Hamilton-Jacobi equations for weakly coupled elliptic systems, (w/ Ari Arapostathis and Prasun Roychowdhury) Journal of Differential Equations, Vol 314, 25 March 2022, Pages 128-160

• Risk-sensitive control for a class of diffusions with jumps, (w/ Ari Arapostathis) Annals of Applied Probability, Vol 32, No. 6, 4106-4142, 2022

• Liouville theorems for infinity Laplacian with  gradient and KPP type equation (w/ Hoang-Hung Vo)  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. XXIV, 2023, 1223-1256

• A study of nonlocal spatially heterogeneous logistic equation with harvesting, (w/ Mitesh Modasiya) Nonlinear Analysis, Volume 214, January 2022, 112599

• A strong maximum principle and a compact support principle for infinity Laplacian,  (in honor of Louis Nirenberg) Pure and Applied Functional Analysis, Vol. 8, no. 1, 103--115, 2023

• Hopf's lemma for viscosity solutions to a class of non-local equations with applications, (w/ József Lörinczi) Nonlinear Analysis, Vol 204, 2021, 112194

• Generalized principal eigenvalues of convex nonlinear elliptic operators in RN (w/ Prasun Roychowdhury) Advances in Calculus of Variations, Vol. 15, No. 4 , 673--691, 2022.

• Regularity results of nonlinear perturbed stable-like operators (w/ Mitesh Modasiya) Differential and Integral Equations, Vol 33, 597--624, 2020

• A variational characterization of the risk-sensitive average reward for controlled diffusions on Rd, (w/ Ari Arapostathis, Vivek Borkar and Suresh Kumar) SIAM Journal of Control and Optimization, Vol. 58(6), 3785–-3813, 2020

• On the policy improvement algorithm for ergodic risk-sensitive control, (w/ Ari Arapostathis, Somnath Pradhan) Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol 151, 1305–1330, 2021

• Ambrosetti-Prodi type results for Dirichlet problems of the fractional Laplacian-like operators, (w/ József Lörinczi) Integral Equations and Operator Theory 92, 2020.

• Integral representation using Green function for fractional Hardy equations (w/ Mousomi Bhakta, Debdip Ganguly, Luigi Montoro), Journal of Differential Equations, 269(7), 2020, 5573-5594

• Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces, (w/ Janna Lierl) Journal of Functional Analysis 278, 2020

• Principal eigenvalues of a class of nonlinear integro-differential operators,  Journal of Differential Equations 268(9), 5257-5282, 2020

• A variational formula for risk-sensitive control of diffusion in Rd, (w/ Ari Arapostathis) SIAM J. Control and Optimization 58(1), 85--103, 2020

• On overdetermined problems for a general class of nonlocal operators (w/ Sven Jarohs) Journal of Differential Equations, Volume 268, Issue 5, 2368--2393, 2020

• On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient  (w/ Ari Arapostathis, Luis Caffarelli)  Communications in Partial Differential Equations, 44:12, 1466-1480, 2019

• Existence and non-existence results for a class of semilinear nonlocal operators with exterior condition,  Pure and Applied Functional Analysis, Vol 6, 2021, 289-308 (Special issue in memory of Professor Felix E. Browder)

• Maximum principles and Aleksandrov-Bakelman-Pucci type estimates for non-local Schrödinger equations with exterior conditions, (w/ József Lörinczi) SIAM J. of Math Analysis, 51(3), 1543–1581, 2019

• Liouville type results for systems of equations involving fractional Laplacian in exterior domains, Nonlinearity 32, 2246–2268, 2019

• Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators, (w/ József Lörinczi)  J of Diff Equations, 267 , 267-306, 2019

• Maximum principles for time-fractional Cauchy problems with spatially non-local components, (w/ József Lörinczi) Fractional Calculus and Applied Analysis, Vol 21 (5), 1335--1359, 2018

• Certain Liouville properties of eigenfunctions of elliptic operators, (w/ Ari Arapostathis and Debdip Ganguly) Transactions of the AMS, Vol. 371(6), 4377--4409, 2019. (The Arxiv version has an improved lower-bound on the decay of non-negative supersolutions. See Corollary ~4.1)

• Strict monotonicity of principal eigenvalues of elliptic operators in Rd and risk-sensitive control, (w/ Ari Arapostathis and Subhamay Saha) Journal de Mathématiques Pures et Appliquées, Vol 124, 169-219, 2019.

• Zero-sum stochastic differential game with risk-sensitive cost, (w/ Subhamay Saha) Applied Mathematics and Optimization, 81, 113–140, 2020

• Controlled equilibrium selection in stochastically perturbed dynamics, (w/ Ari Arapostathis and Vivek Borkar) Annals of Probability, Vol. 46, No. 5, 2749-2799, 2018

• Law of large numbers for the many-server earliest-deadline-first queue, (w/ Rami Atar, Haya Kaspi) Stochastic Processes and their Applications, Vol 128 (7), 2270-2296, 2018.

• Infinite horizon risk sensitive control of diffusions without any blanket stability assumptions, (w/ Ari Arapostathis) Stochastic Processes and their Applications, Vol 128(5), 1485-1524, 2018.

• A Skorokhod map on measure-valued paths with applications to priority queues, (w/ Rami Atar, Haya Kaspi and Kavita Ramanan) Annals of Applied Probability, Vol. 28 (1), 418--481, 2018.

• Location of maximizers of eigenfunctions of fractional Schrödinger's equation, Mathematical Physics, Analysis and Geometry 20, no. 4, pages 14, 2017.

• An ergodic control problem for many-server multi-class queueing systems with cross-trained servers,  Stochastic Systems 7, no. 2, 263-288, 2017.

• On viscosity solution of HJB equations with state constraints and reflection control, (w/ Hitoshi Ishii, Subhamay Saha and Lin Wang) SIAM J. of Control and Optimization, Vol. 55, No. 1, 365-396, 2017.

• On solutions of mean field games with ergodic cost, (w/ Ari Arapostathis, Johnson Carroll) Journal de Mathématiques Pures et Appliquées 107, 205-251, 2017.

• The Dirichlet problem for stable-like Operators and related probabilistic representations, (w/ Ari Arapostathis and Luis Caffarelli) Communications in PDE, Vol. 41 , No. 9, 1472-1511, 2016. (The arxived paper has a different title and contains more detailed proofs)

• On scaling limits of  power law Shot-noise fields, (w/ François Baccelli) Stochastic Models, Vol 31, No. 2, 187-207, 2015.

• Ergodic control of multi-class M/M/N+M queues in the Halfin-Whitt regime, (w/ Ari Arapostathis and Guodong Pang) Annals of Applied Probability, Vol. 25, No. 6, 3511--3570, 2015.

• Fluid limits of G/G/1+G queues under non-preemptive Earliest-Deadline-First discipline, (w/ Rami Atar and Haya Kaspi) Maths. of Operation Research, Vol. 40, Issue 3, 683--702, 2015. 

• Risk-sensitive control for multi-class many server queues in the moderate deviation regime, Maths. of Operation Research, Vol. 39, No. 3, 908-929, 2014.

• Control of the multiclass G/G/1 queue in the moderate deviation regime, (w/ Rami Atar) Annals of Applied Probability, Vol. 24, No. 5, 2033-2069, 2014. 

• Exit time and invariant measure asymptotics for small noise constrained diffusions, (w/ Amarjit Budhiraja) Stochastic Processes and their Applications 121, no. 5, 899–924, 2011.

• Risk-sensitive control of diffusions with small running cost, Applied Mathematics and Optimization, Vol. 64, No. 1, 1–12, 2011.

• An eigenvalue approach to the risk sensitive control problem in near monotone case, Systems and Control Letters 60, 181-184, 2011.

• On a controlled eigenvalue problem, (w/ Vivek S. Borkar) Systems and Control Letters 59, 734–735, 2010.

• Small noise asymptotics for invariant densities for a class of diffusions : a control theoretic view, (w/ Vivek S. Borkar)  Journal of Math. Analysis and Applications 360. No. 2, 476–484, 2009.(Erratum Arxiv)