Scalar conservation laws with fractional stochastic forcing: Existence, uniqueness and invariant measure

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Saussereau, Bruno¹  Stoica, Ion Lucretiu^2,3 

[1] CNRS, Lab Math Besancon, UMR 6623, F-25030 Besancon, France

[2] Univ Bucharest, Simion Stoilow Romanian Acad, Inst Math, RO-70109 Bucharest, Romania

[3] Univ Bucharest, Fac Math, RO-70109 Bucharest, Romania

关键词: Scalar conservation laws;    Random perturbations;    Variational principle;    Deterministic control theory;    Hamilton-Jacobi-Bellman equation;    Fractional Brownian motion;   

DOI  :  10.1016/j.spa.2012.01.005

来源: Elsevier

【 摘 要 】

We study a fractional stochastic perturbation of a first-order hyperbolic equation of nonlinear type. The existence and uniqueness of the solution are investigated via a Lax-Oleinik formula. To construct the invariant measure we use two main ingredients. The first one is the notion of a generalized characteristic in the sense of Dafermos. The second one is the fact that the oscillations of the fractional Brownian motion are arbitrarily small for an infinite number of intervals of arbitrary length. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free