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.File in questo prodotto:
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