Results 141 to 150 of about 199,250 (207)

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 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

Strong Averaging Principle for Slow–Fast Stochastic Partial Differential Equations with Locally Monotone Coefficients

Applied Mathematics and Optimization, 2019
This paper is devoted to proving the strong averaging principle for slow–fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone ...
Wei Liu, M. Röckner, Xiaobin Sun, Yingchao Xie   +3 more
semanticscholar   +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

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

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

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

Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations

Annals of PDE, 2017
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential equations.
N. Glatt-Holtz, David P. Herzog, Jonathan C. Mattingly   +2 more
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

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