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 $$d\ge 2$$; the case $$d=1$$is also investigated but no conclusive answer is obtained.

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

Galeati L
2020-01-01

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 $$d\ge 2$$; the case $$d=1$$is also investigated but no conclusive answer is obtained.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/244600
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