Results 311 to 320 of about 351,513 (382)

Stochastic partial differential equations

Universitext, 2020
Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
P. Friz, M. Hairer
semanticscholar   +2 more sources

Strong and Weak Convergence Rates of a Spatial Approximation for Stochastic Partial Differential Equation with One-sided Lipschitz Coefficient

SIAM Journal on Numerical Analysis, 2019
Strong and weak approximation errors of a spatial finite element method are analyzed for the stochastic partial differential equations (SPDEs) with one-sided Lipschitz coefficients, including the s...
J. Cui, Jialin Hong
semanticscholar   +1 more source

STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE

Mathematical Models and Methods in Applied Sciences, 1991
Stochastic partial differential equations are proposed in order to model some turbulence phenomena. A particular case (the stochastic Burgers equations) is studied. Global existence of solutions is proved. Their regularity is also studied in detail. It is shown that the solutions cannot possess too high regularity.
Brzeźniak, Z., Capiński, M., Flandoli, F.   +2 more
openaire   +2 more sources

Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups

Mathematica Slovaca, 2019
The aim of this paper is to discuss the existence of mild solutions for a class of semilinear stochastic partial differential equation with nonlocal initial conditions and noncompact semigroups in a real separable Hilbert space.
Xuping Zhang, Pengyu Chen, Ahmed Abdelmonem, Yongxiang Li   +3 more
semanticscholar   +1 more source

Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control

Chinese Annals of Mathematics. Series B, 2016
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation.
M. Tang, Qingxin Meng, Meijiao Wang
semanticscholar   +1 more source

ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Mathematics of the USSR-Sbornik, 1975
In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
openaire   +1 more source

Stochastic Partial Differential Equations

2003
The purpose of this chapter is to give an introduction to stochastic partial differential equations from a computational point of view. The presented tools provide a consistent quantitative way of relating uncertainty in input to uncertainty in output for PDE-based models.
H. P. Langtangen, H. Osnes
openaire   +1 more source

MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic ...
Boufoussi, B., Mrhardy, N.
openaire   +2 more sources

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in Mathematics and Statistics, 2017
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
Weinan E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

Adaptive Concepts for Stochastic Partial Differential Equations

Journal of Scientific Computing, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas Prohl, Christian Schellnegger
openaire   +1 more source