Existence and smoothness of the density for the stochastic continuity\n equation

2018/03/16 by David A. C. Mollinedo, Mollinedo, David A. C., Christian Olivera +3
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1803.06170

openalex publication_date 2018/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the stochastic continuity equation driven by Brownian motion. We\nuse the techniques of the Malliavin calculus to show that the law of the\nsolution has a density with respect to the Lebesgue measure. We also prove that\nthe density is Holder continuous and satisfies some Gaussian-type estimates.\n

Citations

• The density of the solution to the stochastic transport equation with\n fractional noise

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