Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Smoothing effect and Derivative formulas for Ornstein-Uhlenbeck processes driven by subordinated cylindrical Brownian noises (2101.06493v1)

Published 16 Jan 2021 in math.PR

Abstract: We investigate the concept of cylindrical Wiener process subordinated to a strictly $\alpha$-stable L\'evy process, with $\alpha\in\left(0,1\right)$, in an infinite dimensional, separable Hilbert space, and consider the related stochastic convolution. We then introduce the corresponding Ornstein-Uhlenbeck process, focusing on the regularizing properties of the Markov transition semigroup defined by it. In particular, we provide an explicit, original formula -- which is not of Bismut-Elworthy-Li's type -- for the Gateaux derivatives of the functions generated by the operators of the semigroup, as well as an upper bound for the norm of their gradients. In the case $\alpha\in\left(\frac{1}{2},1\right)$, this estimate represents the starting point for studying the Kolmogorov equation in its mild formulation.

Summary

We haven't generated a summary for this paper yet.