Related papers: Distribution Dependent Stochastic Differential Equ…

Stochastic differential equations with Levy motion arise the mathematical models for various phenomenon in geophysical and biochemical sciences. The Fokker Planck equation for such a stochastic differential equations is a nonlocal partial…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

In this paper, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations (anticipated BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution $(Y,…

A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…

Using the generalized variational framework, the strong/weak existence and uniqueness of solutions are derived for a class of distribution dependent stochastic porous media equations on general measure spaces, which also extends the…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

Rough stochastic differential equations (rough SDEs), recently introduced by Friz, Hocquet and L\^e in arXiv:2106.10340, have emerged as a versatile tool to study "doubly" SDEs under partial conditioning (with motivation from pathwise…

The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

Distribution dependent stochastic differential equations have been a very hot subject with extensive studies. On the other hand, under the $G$-expectation framework, stochastic differential equations driven by $G$-Brownian motion (in short…

We propose a new type SDE depending on the future distributions with all initial values, and establish the correspondence between this equation and the associated singular nonlinear PDE. Well-posedness and regularities are investigated.

We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the…

Marcus stochastic delay differential equations (SDDEs) are often used to model stochastic dynamical systems with memory in science and engineering. Since no infinitesimal generators exist for Marcus SDDEs due to the non-Markovian property,…

This paper studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker-Planck equations for QSDs. Similar as the case of Fokker-Planck equations for invariant…

Our aim is to study the well-posedness of quasilinear stochastic partial differential equations driven by G-Brownian motion (GSPDEs for short) and the associated backward doubly stochastic differential equations (GBDSDEs for short). We…