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This paper delves into the well-posedness and the numerical approximation of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear local Lipschitz coefficients that satisfy the more general monotonicity condition…

This work investigates numerical approximations of index 1 stochastic differential algebraic equations (SDAEs) with non-constant singular matrices under non-global Lipschitz conditions. Analyzing the strong convergence rates of numerical…

We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge…

In this paper, we study the well-posedness and regularity of non-autonomous stochastic differential algebraic equations (SDAEs) with nonlinear, locally Lipschitz and monotone (2) coefficients of the form (1). The main difficulty is the fact…

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…

We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…

We propose a new numerical scheme for Backward Stochastic Differential Equations based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the…

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…

We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is…

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…

Existing fundamental theorems for mean-square convergence of numerical methods for stochastic differential equations (SDEs) require globally or one-sided Lipschitz continuous coefficients, while strong convergence results under merely local…

In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…

Existence, uniqueness, and $L_p$-approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients…

We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…

In this paper, a weak Local Linearization scheme for Stochastic Differential Equations (SDEs) with multiplicative noise is introduced. First, for a time discretization, the solution of the SDE is locally approximated by the solution of the…

In this paper, we apply the tamed technique to the Milstein numerical scheme to investigate Neutral Stochastic Delay Differential Equations(NSDDEs) with highly nonlinear coefficients. Under the local Lipschitz condition and Khasminskii…

The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration…

In this article we introduce several kinds of easily implementable explicit schemes, which are amenable to Khasminski's techniques and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…