32 citations · 33 across the 7 of their papers we have counts for
9 papers
On the rate of convergence for monotone numerical schemes for nonlocal Isaacs' equations
Imran H. Biswas, Indranil Chowdhury, Espen R. Jakobsen
We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equ…
On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
Imran H. Biswas, Ananta K. Majee, Guy Vallet
In this article we deal with stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasise is on analysing the effect of multiplic…
Continuous dependence estimate for conservation laws with Lévy noise
Imran H. Biswas, Ujjwal Koley, Ananta K. Majee
We are concerned with multidimensional stochastic balance laws driven by Lévy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an…
On the differentiability of the solutions of non-local Isaacs equations involving -Laplacian
Imran H Biswas, Indranil Chowdhury
We derive -estimate for the solutions of a class of non-local elliptic Bellman-Isaacs equations. These equations are fully nonlinear and are associated with infinite horiz…
Conservation laws driven by Lévy white noise
Imran H. Biswas, Kenneth H. Karlsen, Ananta K. Majee
We consider multidimensional conservation laws perturbed by multiplicative Lévy noise. We establish existence and uniqueness results for entropy solutions. The entropy inequalities…
Stochastic conservation laws: weak-in-time formulation and strong entropy condition
Imran H. Biswas, Ananta K. Majee
This article is an attempt to complement some recent developments on conservation laws with stochastic forcing. In a pioneering development, Feng $&$ Nualarthave developed the entr…
Regularization by 1/2-Laplacian and vanishing viscosity approximation of HJB equations
Imran H. Biswas
We investigate the regularizing effect of adding small fractional Laplacian, with critical fractional exponent 1/2, to a general first order HJB equation. Our results include some…
On zero-sum Stochastic Differential Games with Jump-Diffusion driven state: A viscosity solution framework
Imran H. Biswas
A zero-sum differential game with controlled jump-diffusion driven state is considered, and studied using a combination of dynamic programming and viscosity solution techniques. We…
Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE
I. H. Biswas, E. R. Jakobsen, K. H. Karlsen
We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Levy (jump-diffusion) processes. These equations are fully non-linear, degenerate p…