Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
type: Item
instance of: scholarly article
title: Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
zbMATH Open document ID: 1060.70025
DOI: 10.4171/RMI/392
author: Vassili Kolokoltsov
author: A. E. Tyukov
author: R. L. Schilling
published in: Revista Matemática Iberoamericana
publication date: 2004-10-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39720
review text: This paper is devoted to the study of stochastic Hamilton-Jacobi equation \[ dS+H \biggl(x,\frac{\partial S}{\partial x}\biggr)\,dt+c(x)\,d\xi_t=0,\quad x\in\mathbb{R}^d,\;t>0,\tag{1} \] and of the corresponding Hamilton system \[ \begin{aligned} dx&=\frac{\partial H}{\partial p}dt,\\ dp&=-\frac{\partial H}{\partial x}dt-\frac{\partial c}{\partial x}d\xi_t, \end{aligned}\tag{2} \] where \(\xi_t\) is a Lévy noise without Brownian part. The authors first prove the well-posedness of a suitable boundary value problem for (2), and then use this result to implement a stochastic version of the classical method of characteristics for Hamilton-Jacobi equation (1).
reviewed by: Fabio Bagagiolo
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 2110190
zbMATH Keywords: Lévy noise
zbMATH Keywords: well-posedness
zbMATH Keywords: method of characteristics
MaRDI profile type: Publication
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OpenAlex ID: W1978788369
description: scientific article; zbMATH DE number 2110190