Work

Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure

Year: 2025

Type: article

Abstract: We show weak existence and uniqueness in law for a general class of stochastic differential equations in $$\mathbb {R}^d$$ R d , $$d\ge 1$$ d ≥ 1 , with prescribed sub-invariant measure $$\widehat{\mu }$$ μ ^ . The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate and discontinuous, and locally unbounded, respectively. Uniqueness in law is obtained via $$L^1({\mathbb {R}}^d,\widehat{\mu })$$ L 1 ( R d , μ ^ ) -uniqueness in a subclass of continuous Markov processes, namely right processes that have $$\widehat{\mu }$$ μ ^ as sub-invariant measure and have continuous paths for $$\widehat{\mu }$$ μ ^ -almost every starting point. Weak existence is obtained for a broader class via the martingale problem, by first constructing a sub-Markovian $$C_0$$ C 0 -semigroup of contractions with respect to $$\widehat{\mu }$$ μ ^ and then applying generalized Dirichlet form theory.

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-025-01076-8

Authors: Haesung Lee, Gerald Trutnau

Institutions: Kumoh National Institute of Technology, Seoul National University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: National Research Foundation, Seoul National University, Ministry of Science, ICT and Future Planning, National Research Foundation of Korea