On the convergence of stochastic transport equations to a deterministic parabolic one

Lucio Galeati

On the convergence of stochastic transport equations to a deterministic parabolic one

Probability 2019-11-27 v2

Authors: Lucio Galeati

Abstract

A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution of a deterministic parabolic equation. Existence and uniqueness for STLE are also discussed. Our method works in dimension $d\geq 2$ ; the case $d=1$ is also investigated but no conclusive answer is obtained.

Keywords

stochastic transport equation multiplicative noise renormalization deterministic parabolic equation convergence existence and uniqueness

Cite

@article{arxiv.1902.06960,
  title  = {On the convergence of stochastic transport equations to a deterministic parabolic one},
  author = {Lucio Galeati},
  journal= {arXiv preprint arXiv:1902.06960},
  year   = {2019}
}

Comments

Only minor modifications, main results unchanged; several references added and the paragraph at the beginning of Section 4.2 extended

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