Hypercontractivity for Functional Stochastic Differential Equations

2014/06/30 by Jianhai Bao, Bao, Jianhai, Feng‐Yu Wang +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1406.7580

openalex publication_date 2014/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup P_t converges exponentially to its unique invariant probability measure μ in entropy, L²(μ) and the totally variational norm, and it is compact in L²(μ) for large t>0. This provides a natural class of non-symmetric Markov semigroups which are compact for large time but non-compact for small time. A semi-linear model which may not satisfy this sufficient condition is also investigated.

Citations

• Hypercontractivity for Stochastic Hamiltonian Systems

Cited by

• Exponential Ergodicity in Relative Entropy and L²-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs

Related

• Hypercontractivity for Functional Stochastic Partial Differential Equations
• Hypercontractivity and Its Applications for Functional SDEs of Neutral Type
• Functional Inequalities for Non-Symmetric Stochastic Differential Equations
• Hypercontractivity for Stochastic Hamiltonian Systems
• A supersolutions perspective on hypercontractivity