Stochastic integration in quasi-Banach spaces
Volume 269 / 2023
Studia Mathematica 269 (2023), 1-64
MSC: Primary 60H05; Secondary 46A16, 60B11.
DOI: 10.4064/sm180424-31-10
Published online: 19 December 2022
Abstract
We develop a stochastic integration theory for processes with values in a quasi-Banach space. The integrator is a cylindrical Brownian motion. The main results give sufficient conditions for stochastic integrability. They are natural extensions of known results in the Banach space setting. We apply our main results to the stochastic heat equation where the forcing terms are assumed to have Besov regularity in the space variable with integrability exponent $p\in (0,1]$. The latter is natural to consider for its potential application to adaptive wavelet methods for stochastic partial differential equations.
