Related papers: On Explicit Stochastic Differential Algebraic Equa…
In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there exist stochastic differential equations (SDEs) with…
In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving…
In this paper, we consider optimal control of stochastic differential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In…
This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…
This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit…
Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic…
The time evolution of probability densities for solutions to stochastic differential equations (SDEs) without delay is usually described by Fokker-Planck equations, which require the adjoint of the infinitesimal generator for the solutions.…
In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the…
In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of…
We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the…
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one…
This article introduces a framework for measuring the uncertain behaviour of a changing system in terms of the solution of a class of fractional stochastic differential equations (fsDEs). This is accomplished via operational matrices based…