Results 271 to 280 of about 579,758 (339)

Stochastic differential equations

2011
In this chapter we present some basic results on stochastic differential equations, hereafter shortened to SDEs, and we examine the connection to the theory of parabolic partial differential equations.
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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

Optimal controls for second‐order stochastic differential equations driven by mixed‐fractional Brownian motion with impulses

Mathematical methods in the applied sciences, 2020
We study optimal control problems for a class of second‐order stochastic differential equation driven by mixed‐fractional Brownian motion with non‐instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed
Rajesh Dhayal, Muslim Malik, Syed Abbas, A. Debbouche   +3 more
semanticscholar   +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 ...
Weinan E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

Stochastic Differential Equations

2016
Let \(\mathbf{W} = (W^{1},\ldots,W^{m})\) be an m-dimensional Brownian motion, and let $$\displaystyle{\boldsymbol{\sigma }= (\sigma _{ij})_{1\leq i\leq d,1\leq j\leq m}: [0,\infty ) \times \mathbb{R}^{d} \rightarrow \mathbb{R}^{d} \times \mathbb{R}^{m}}$$ and $$\displaystyle{\boldsymbol{\mu }= (\mu ^{1},\ldots,\mu ^{d}): [0,\infty ) \times \
Paola Lecca, Angela Re, Adaoha Ihekwaba, Ivan Mura, Thanh-Phuong Nguyen   +4 more
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Stochastic differential equations

Physics Reports, 1976
Abstract In chapter I stochastic differential equations are defined and classified, and their occurrence in physics is reviewed. In chapter II it is shown for linear equation show a differential equation for the averaged solution is obtained by expanding in ατ c , where α measures the size of the fluctuations and τ c their autocorrelation time. This
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Applied Stochastic Differential Equations

, 2019
The topic of this book is stochastic differential equations (SDEs). As their name suggests, they really are differential equations that produce a different “answer” or solution trajectory each time they are solved.
Simo Särkkä, A. Solin
semanticscholar   +1 more source

Stochastic partial differential equations

2014
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.
Peter K. Friz, Martin Hairer
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Variational Inference for Stochastic Differential Equations

Annals of Physics, 2019
The statistical inference of the state variable and the drift function of stochastic differential equations (SDE) from sparsely sampled observations are discussed herein.
M. Opper
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Computational scheme for solving nonlinear fractional stochastic differential equations with delay

Stochastic Analysis and Applications, 2019
This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation.
Behrouz Parsa Moghaddam, A. Mendes Lopes, J. T. Tenreiro Machado, Z. S. Mostaghim   +3 more
semanticscholar   +1 more source