Published March 2019 | Version v1
Journal article

Existence and Smoothness of the Density for the Stochastic Continuity Equation

  • 1. Universidade Tecnológica Federal do Parana (Brazil)
  • 2. Universidade Estadual de Campinas, Departamento de Matemática (Brazil)
  • 3. Université de Lille 1, UFR Mathématiques (France)

Description

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 Hölder continuous and satisfies some Gaussian-type estimates.

Additional details

Identifiers

Publishing Information

Journal Title
Results in Mathematics
Journal Volume
74
Journal Issue
1
Journal Page Range
p. 1-15
ISSN
1422-6383

INIS

Country of Publication
Switzerland
Country of Input or Organization
International Atomic Energy Agency (IAEA)
INIS RN
51103248
Subject category
S97: MATHEMATICAL METHODS AND COMPUTING;
Descriptors DEI
BROWNIAN MOVEMENT; CONTINUITY EQUATIONS; DENSITY; ROUGHNESS; SMOOTH MANIFOLDS; STOCHASTIC PROCESSES
Descriptors DEC
DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL MANIFOLDS; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES; SURFACE PROPERTIES

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Copyright
Copyright (c) 2019 Springer Nature Switzerland AG