On temporal regularity of stochastic convolutions in 2-smooth Banach spaces

Martin Ondrejat; Mark Veraar

doi:10.1214/19-AIHP1017

On temporal regularity of stochastic convolutions in 2-smooth Banach spaces

Martin Ondrejat, Mark Veraar

Analysis

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Abstract

We show that paths of solutions to parabolic stochastic differential equations have the same regularity in time as the Wiener process (as of the current state of art). The temporal regularity is considered in the Besov-Orlicz space Bϕ ^1/₂²_∞(0,T;X)where ϕ₂(x)= exp(x²)− 1 and X is a 2-smooth Banach space.

Original language	English
Pages (from-to)	1792-1808
Number of pages	17
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	56
Issue number	3
DOIs	https://doi.org/10.1214/19-AIHP1017
Publication status	Published - 2020

Keywords

2-smooth Banach space
Besov-Orlicz space
Stochastic convolution
Temporal regularity

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AIHP1017Final published version, 273 KB

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KW - Besov-Orlicz space

KW - Stochastic convolution

KW - Temporal regularity

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On temporal regularity of stochastic convolutions in 2-smooth Banach spaces

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