Coupling in the Heisenberg group and its applications to gradient estimates
| Autor: | Sayan Banerjee, Maria Gordina, Phanuel Mariano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
non-Markovian coupling 01 natural sciences Upper and lower bounds Heisenberg group gradient estimate 010104 statistics & probability Total variation Coupling Mathematics::Probability FOS: Mathematics sub-Riemannian manifold 0101 mathematics 60D05 Brownian motion Mathematics total variation distance Probability (math.PR) 010102 general mathematics Mathematical analysis Karhunen–Loeve expansion Harmonic function Hypoelliptic operator Statistics Probability and Uncertainty 60H30 Laplace operator Mathematics - Probability |
| Zdroj: | Ann. Probab. 46, no. 6 (2018), 3275-3312 |
| Popis: | We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling such as estimates on the coupling rate, and upper and lower bounds on the total variation distance between the laws of the Brownian motions. Finally we use these properties to prove gradient estimates for harmonic functions for the hypoelliptic Laplacian which is the generator of Brownian motion in the Heisenberg group. 42 pages. To appear in Annals of Probability |
| Databáze: | OpenAIRE |
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