Results 11 to 20 of about 199,250 (207)

Invariant manifolds for stochastic partial differential equations

The Annals of Probability, 2003
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant
Duan, Jinqiao, Lu, Kening, Schmalfuss, Björn   +2 more
openaire   +6 more sources

Well-posedness of stochastic partial differential equations with fully local monotone coefficients [PDF]

Mathematische Annalen, 2022
Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple V⊆H⊆V∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
Michael Röckner, Shijie Shang, Tusheng Zhang   +2 more
semanticscholar   +1 more source

Strong approximation of monotone stochastic partial differential equations driven by white noise

IMA Journal of Numerical Analysis, 2020
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second-order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen–Cahn equation, driven by an additive space ...
Zhihui Liu, Zhonghua Qiao
semanticscholar   +1 more source

Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations

Mathematics, 2016
Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed.
Yanmei Liu, Monzorul Khan, Yubin Yan
doaj   +1 more source

On Some Results of the Nonuniqueness of Solutions Obtained by the Feynman–Kac Formula

Mathematics, 2023
The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics.
Byoung Seon Choi, Moo Young Choi
doaj   +1 more source

Real-time reduced-order modeling of stochastic partial differential equations via time-dependent subspaces [PDF]

Journal of Computational Physics, 2019
We present a new methodology for the real-time reduced-order modeling of stochastic partial differential equations called the dynamically/bi-orthonormal (DBO) decomposition.
Prerna Patil, H. Babaee
semanticscholar   +1 more source

SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions

Journal of Function Spaces, 2016
The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by ...
Pengju Duan
doaj   +1 more source

Existence and stability of mild solutions to parabolic stochastic partial differential equations driven by Lévy space-time noise

Electronic Journal of Qualitative Theory of Differential Equations, 2016
This paper is concerned with well-posedness and stability of parabolic stochastic partial differential equations. Firstly, we obtain some sufficient conditions ensuring the existence and uniqueness of mild solutions, and some $\mathcal{H}$-stability ...
Chaoliang Luo, Shangjiang Guo
doaj   +1 more source

Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning

Mathematics, 2023
Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in high-
Xiangdong Liu, Yu Gu
doaj   +1 more source

Averaging principle for slow-fast stochastic partial differential equations with Hölder continuous coefficients [PDF]

Journal of Differential Equations, 2019
By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H\"{o}lder continuous drift ...
Xiaobin Sun, Longjie Xie, Yingchao Xie
semanticscholar   +1 more source