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Hölder Regularity and Gradient Estimates for Sdes Driven by Cylindrical Α-stable Processes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zhang, Xicheng |
| Copyright Year | 2020 |
| Abstract | We establish Hölder regularity and gradient estimates for the transition semigroup of the solutions to the following SDE: dXt = σ(t, Xt−)dZt + b(t, Xt)dt, X0 = x ∈ R , where (Zt)t>0 is a d-dimensional cylindrical α-stable process with α ∈ (0, 2), σ(t, x) : R+ ×R → R ⊗R is bounded measurable, uniformly nondegenerate and Lipschitz continuous in x uniformly in t, and b(t, x) : R+ × R → R is bounded β-Hölder continuous in x uniformly in t with β ∈ [0, 1] satisfying α + β > 1. Moreover, we also show the existence and regularity of the distributional density of X(t, x). Our proof is based on Littlewood-Paley’s theory. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/2001.03873 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
