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

Bruno Saussereau and Ion Lucretiu Stoica

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1456-1486

Abstract: 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–Oleĭnik 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.

Keywords: Scalar conservation laws; Random perturbations; Variational principle; Deterministic control theory; Hamilton–Jacobi–Bellman equation; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2012.01.005

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