Lp-valued stochastic convolution integral driven by Volterra noise-Reference-Cited by-同舟云学术

Lp-valued stochastic convolution integral driven by Volterra noise

Published:2018-10-29 Issue:06 Volume:18 Page:1850048
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

Čoupek Petr¹,Maslowski Bohdan¹,Ondreját Martin²

Affiliation:

1. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8, 186 75, Czech Republic

2. Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou věží 4, Prague 8, 182 08, Czech Republic

Abstract

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space [Formula: see text]. The corresponding regularity is obtained by showing that the stochastic convolution integrals are Hölder continuous in a suitable function space. In particular cases, this allows us to show space-time Hölder continuity of the solution. The main tool used is a hypercontractivity result on Banach-space valued random variables in a finite Wiener chaos.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949371850048X

Reference26 articles.

1. Stochastic Calculus with Respect to Gaussian Processes

2. Stochastic integration with respect to the fractional Brownian motion

3. Equivalence of Volterra processes

4. The space LP, with mixed norm

5. Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise

Cited by 15 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Harnack inequalities for functional SDEs driven by subordinate Volterra-Gaussian processes;Stochastic Analysis and Applications;2024-04

2. Ergodicity of increments of the Rosenblatt process and some consequences;Czechoslovak Mathematical Journal;2024-03-07

3. Stochastic integration with respect to fractional processes in Banach spaces;Journal of Functional Analysis;2022-04

4. On a generalized stochastic Burgers' equation perturbed by Volterra noise;Journal of Mathematical Analysis and Applications;2022-02

5. Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses;Chaos, Solitons & Fractals;2021-10