Liouville's equations for random systems

• Published in: Stochastic analysis and applications Vol. 40; no. 6; pp. 1026 - 1047
• Main Author: Jornet, Marc
• Format: Journal Article
• Language: English
• 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

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...