A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has
become prominent. A forward diffusion process adds gradually noiseto data, while a model …

In this paper, a class of new Magnus-type methods is proposed for non-commutative Itô
stochastic differential equations (SDEs) with semi-linear drift term and semi-linear diffusion …

In this article, a new class of stochastic exponential Runge-Kutta (SERK) methods is
developed for solving stochastic differential equations. The proposed SERK methods can …

We propose explicit stochastic Runge–Kutta (RK) methods for high-dimensional Itô
stochastic differential equations. By providing a linear error analysis and utilizing a Strang …

In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes
for the numerical discretization of highly oscillatory stochastic differential equations. These …

We discuss a system of stochastic differential equations with a stiff linear term and additive
noise driven by fractional Brownian motions (fBms) with Hurst parameter H> 1 2, which arise …

In recent papers, a simple harmonic oscillator with additive noise has been studied by
several researchers, and it has been shown that its mean total energy increases linearly as …

In this paper a set of previous general results for the development of B--series for a broad
class of stochastic differential equations has been collected. The applicability of these …

We introduce a tamed exponential time integrator which exploits linear terms in both the drift
and diffusion for Stochastic Differential Equations (SDEs) with a one sided globally Lipschitz …

In this paper, we investigate the strong convergence of the exponential Euler method to
stochastic delay differential equations with fractional Brownian motion (FSDDEs) of Hurst …