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

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  • Saussereau, Bruno
  • Stoica, Ion Lucretiu

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.

Suggested Citation

  • Saussereau, Bruno & Stoica, Ion Lucretiu, 2012. "Scalar conservation laws with fractional stochastic forcing: Existence, uniqueness and invariant measure," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1456-1486.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1456-1486
    DOI: 10.1016/j.spa.2012.01.005
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    References listed on IDEAS

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    1. Hult, Henrik, 2003. "Approximating some Volterra type stochastic integrals with applications to parameter estimation," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 1-32, May.
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