Related papers: A note on Euler approximations for stochastic diff…

In this paper we study the stochastic inhomogeneous incompressible Euler equations in the whole space $\RR^3$. We prove the existence and pathwise uniqueness of local solutions with both additive and multiplicative stochastic noise. Our…

The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by c\`adl\`ag paths satisfying a suitable criterion, namely the…

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second…

We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method…

This paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow and fast variables, and…

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

In this paper, we investigate new sufficient conditions to ensure the existence of a unique global strong solution of stochastic differential equations with jumps. By using Euler approximation and by utilising a new test function…

In this note, we derive an existence and uniqueness results for delayed backward stochastic differential equation with only integrable data.

We study the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We prove the existence of a statistically stationary solution in the class of weak…

In this paper, the successive approximation method is applied to investigate the existence and uniqueness of solutions to the stochastic differential equations (SDEs) driven by L\'evy noise under non-Lipschitz condition which is a much…

We study strong approximation of $d$-dimensional stochastic differential equations (SDEs) with a discontinuous drift coefficient. More precisely, we essentially assume that the drift coefficient is piecewise Lipschitz continuous with an…

In this paper, we get some convergence rates in total variation distance in approximating discretized paths of L{\'e}vy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of…

In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local…

This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g.,…

In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…

We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on…

For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…

The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with…

We analyse errors of randomized explicit and implicit Euler schemes for approximate solving of ordinary differential equations (ODEs). We consider classes of ODEs for which the right-hand side functions satisfy Lipschitz condition globally…

In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant…