Existence and smoothness of the density for the stochastic continuity equation
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🧮 math.PR
math.AP
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densitycontinuityequationstochasticbrowniancalculusconsidercontinuous
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We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the density is Holder continuous and satisfies some Gaussian-type estimates.
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