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We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is replaced by a condition that holds almost surely and mixes…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional…
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative…
Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces allowing the derivatives of the…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
It is shown that some class of differential inclusions has solutions that are defined and bounded for all real values of independent variable. Applications to dynamics are considered.
We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives with nonlocal boundary conditions. We investigate the Green function and some of its…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the…
The paper deals with an integrodifferential operator which models numerous phenomena in superconductivity, in biology and in viscoelasticity. Initialboundary value problems with Neumann, Dirichlet and mixed boundary conditions are analyzed.…
This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space $\mathcal N^\infty$ of stochastic processes of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified with…
This paper is concerned with solution in H\"{o}lder spaces of the Cauchy problem for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown variables are viewed as…
We derive a functional change of variable formula for {\it non-anticipative} functionals defined on the space of right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…