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Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 22 July 2020Accepted: February 2021Published online: 20 May 2021Keywordsstability estimates, hypoelliptic operators, wave equation, resolvent approximate observabilityAMS Subject Headings35H10, 35B60, 35L05, 93B07, 93B05Publication DataISSN (print): 0363-0129ISSN (online)...

We study semigroups generated by general fractional Ornstein–Uhlenbeck operators acting on $$L^2({\mathbb {R}}^n)$$ . characterize geometrically the partial Gevrey-type smoothing properties of these semigroups, and we sharply describe blow-up associated seminorms for short times, generalizing hypoelliptic quadratic cases. As a byproduct this study, establish subelliptic estimates enjoyed whole ...

We provide a condition for f -ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift inequality on the extended generator and on the resolvent kernel are given. Results related to (f, r)-regularity and to moderate deviation principle for int...

We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H > 1 2 have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems satisfy a suitable version of the strong Feller property and we conclude that the...

In an interesting note, E.M. Stein observed some 20 years ago that while the Kohn Laplacian b on functions is neither locally solvable nor (analytic) hypoelliptic, the addition of a non-zero complex constant reversed these conclusions at least on the Heisenberg group, and Kwon reproved and generalized this result using the method of concatenations. Recently Hanges and Cordaro have studied this ...