Related papers: On the Solution of Stochastic Functional Different…
We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for…
Numerical methods for stochastic differential equations with non-globally Lipschitz coefficients are currently studied intensively. This article gives an overview of our work for the case that the drift coefficient is potentially…
We survey recent developments in the field of complexity of pathwise approximation in $p$-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion.…
A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
We explore Ito stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of…
In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz…
For time-homogeneous stochastic differential equations (SDEs) it is enough to know that the coefficients are Lipschitz to conclude existence and uniqueness of a solution, as well as the existence of a strongly convergent numerical method…
In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential…
Under a mild Lipschitz condition we prove a theorem on the existence and uniqueness of global solutions to delay fractional differential equations. Then, we establish a result on the exponential boundedness for these solutions.
We consider a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with coinvariant derivatives and a right-end boundary condition. Such problems arise naturally in the study of properties of the value functional in…
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…
We extend some methods developed by Albeverio, Brze\'{z}niak and Wu and we show how to apply them in order to prove existence of global strong solutions of stochastic differential equations with jumps, under a local one-sided Lipschitz…
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…
We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated…
Spatial differentiability of solutions of stochastic differential equations (SDEs) is a classical question in stochastic analysis. The case of coefficients with globally Lipschitz continuous derivatives is well understood in the literature.…
In this paper, we study a functional fully coupled forward-backward stochastic differential equations (FBSDEs). Under a new type of integral Lipschitz and monotonicity conditions, the existence and uniqueness of solutions for functional…