Results 251 to 260 of about 208,713 (299)

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 ...
W. E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

Stochastic Partial Differential Equations

2015
A natural generalisation of the finite-dimensional diffusions are stochastic partial differential equations. In this chapter we focus on the Allen-Cahn equation introduced in Section 5.7 in one spatial dimension. Section 5.7 gives the main theorem and a rough outline of its proof.
Anton Bovier, Frank den Hollander
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

Stochastic averaging for two-time-scale stochastic partial differential equations with fractional Brownian motion

Nonlinear Analysis: Hybrid Systems, 2019
In this paper, we are concerned with a class of stochastic partial differential equations that have a slow component driven by a fractional Brownian motion with Hurst parameter 0 H 1 ∕ 2 and a fast component driven by a fast-varying diffusion.
Zhi Li, Litan Yan
semanticscholar   +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

Robust control of parabolic stochastic partial differential equations under model uncertainty

European Journal of Control, 2019
The present paper is devoted to the study of robust control problems of parabolic stochastic partial differential equations under model uncertainty.
Ioannis Baltas, A. Xepapadeas, A. Yannacopoulos   +2 more
semanticscholar   +1 more source

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

Stochastics and Partial Differential Equations: Analysis and Computations, 2018
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener process.
Zhihui Liu, Zhonghua Qiao
semanticscholar   +1 more source

On stochastic partial differential equations with Unbounded coefficients

Potential Analysis, 1992
Existence, uniqueness and approximations of parabolic Itô equations are considered. The well-weighted Sobolev spaces are used. In particular stochastic partial differential equations (SPDE) with unbounded coefficients, SPDE whose coefficients grow faster than linear functions and SPDE on manifolds are discussed.
Gyöngy, István, Krylov, Nicolai V.
openaire   +1 more source

INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we study the existence of an invariant foliation for a class of stochastic partial differential equations with a multiplicative white noise. This invariant foliation is used to trace the long term behavior of all solutions of these equations.
Lu, Kening, Schmalfuß, Björn
openaire   +1 more source

Fully Nonlinear Stochastic Partial Differential Equations

SIAM Journal on Mathematical Analysis, 1996
The authors are concerned with the following stochastic partial differential equation: \[ du(t, .)= L(t, ., u, Du, D^2u) dt+ \langle b(t, .)Du+ h(t, .)u, dW(t) \rangle, \qquad u(0)= u_0, \tag{1} \] where \(L\), \(b\) and \(h\) are suitable functions and \(W\) is an \(\mathbb{R}^N\)-valued Brownian motion.
G. Da Prato, Tubaro, Luciano
openaire   +3 more sources