Related papers: On the reconstruction of diffusions from first-exi…

A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…

We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…

Consider jump-type stochastic differential equations with the drift, diffusion and jump terms. Logarithmic derivatives of densities for the solution process are studied, and the Bismut-Elworthy-Li type formulae can be obtained under the…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

In recent years, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space has begun. In many of these results it is assumed that the drift…

Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

The exponential contraction in $L^1$-Wasserstein distance and exponential convergence in $L^q$-Wasserstein distance ($q\geq 1$) are considered for stochastic differential equations with irregular drift. When the irregular drift drift is…

We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…

We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a L\'evy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown…

This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts…

We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions…

We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with different initial distributions. The primary objective is to construct an accurate and…

This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…

We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…

First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to…

A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…

We prove existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of…