Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise. (30th July 2022)

• Record Type: Journal Article
• Authors: An, Zihao; Zong, Gaofeng
• Other Names: Boulaaras Salah Mahmoud Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-07-30
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/5464688
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : By constructing a coupling with unbounded time-dependent drift, a lower bound estimate of dimension-free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise. The key is an application of the inverse Hölder inequality. Combining this with the well-known upper bound, bilateral dimension-free Harnack inequality with power is established. As a dual inequality, the bilateral shift-Harnack inequalities with power are also investigated for stochastic differential equation with additive noise. Applications to the study of heat kernel inequalities are provided to illustrate the obtained inequalities.