Liouville's equations for random systems

Given a random system, a Liouville's equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this article, we derive Liouville's equations for the first-order homogeneous semilinear random partial differential...

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Published inStochastic analysis and applications Vol. 40; no. 6; pp. 1026 - 1047
Main Author Jornet, Marc
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.11.2022
Taylor & Francis Ltd
Subjects
Fields (mathematics)
Liouville's equation
Mathematical analysis
ordinary and fractional differential equation
Partial differential equations
Probability density function
Probability density functions
random partial
Stochastic processes
Online AccessGet full text
ISSN0736-2994
1532-9356
DOI10.1080/07362994.2021.1980015

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Abstract Given a random system, a Liouville's equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this article, we derive Liouville's equations for the first-order homogeneous semilinear random partial differential equation. This is done for all finite-dimensional distributions of the random field solution, starting with dimension one, then dimension two, and finally generalizing to any dimension. Several examples, including the linear advection equation with random coefficients, are treated. As a corollary, we deduce Liouville's equations for path-wise stochastic integrals and nonlinear random ordinary differential equations.
AbstractList Given a random system, a Liouville's equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this article, we derive Liouville's equations for the first-order homogeneous semilinear random partial differential equation. This is done for all finite-dimensional distributions of the random field solution, starting with dimension one, then dimension two, and finally generalizing to any dimension. Several examples, including the linear advection equation with random coefficients, are treated. As a corollary, we deduce Liouville's equations for path-wise stochastic integrals and nonlinear random ordinary differential equations.
Author Jornet, Marc
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crossref_primary_10_1016_j_jmps_2023_105491
crossref_primary_10_1016_j_amc_2023_128197
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Snippet Given a random system, a Liouville's equation is an exact partial differential equation that describes the evolution of the probability density function of the...
Given a random system, a Liouville’s equation is an exact partial differential equation that describes the evolution of the probability density function of the...
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SubjectTerms Fields (mathematics)
Liouville's equation
Mathematical analysis
ordinary and fractional differential equation
Partial differential equations
Probability density function
Probability density functions
random partial
Stochastic processes
Title Liouville's equations for random systems
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