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
Optional Information
- Copyright
- Copyright (c) 2019 Springer Nature Switzerland AG