Related papers: Stoch-IDENT: New Method and Mathematical Analysis …
In this paper, we introduce a new simple approach to developing and establishing the convergence of splitting methods for a large class of stochastic differential equations (SDEs), including additive, diagonal and scalar noise types. The…
Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the algorithms derived by Kloeden, Platen,…
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
This book is an introduction to the theory of stochastic partial differential equations (SPDEs), using the random field approach pioneered by J.B. Walsh (1986). It consists of two blocks: the core matter (Chapters 1 to 6) and the appendices…
We consider a process given as the solution of a one-dimensional stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
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…
We study identifiability in continuous-time linear stationary stochastic differential equations with known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's…
Solving elliptic partial differential equations (PDEs) is a fundamental step in various scientific and engineering studies. As a classic stochastic solver, the Walk-on-Spheres (WoS) method is a well-established and efficient algorithm that…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Moment estimation for stochastic differential equations (SDEs) is fundamental to the formal reasoning and verification of stochastic dynamical systems, yet remains challenging and is rarely available in closed form. In this paper, we study…
A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…
The quasi-potential is a key concept in stochastic systems as it accounts for the long-term behavior of the dynamics of such systems. It also allows us to estimate mean exit times from the attractors of the system, and transition rates…
This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…
Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…