English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We provide a version of the stochastic Fubini's theorem which does not dependon the particular stochastic integrator chosen as far as the stochasticintegration is built as a continuous linear operator from an $L^p$ space ofBanach space-valued processes (the stochastically integrable processes) to an$L^p$ space of Banach space-valued paths (the integrated processes). Then, forintegrators on a Hilbert space $H$, we consider stochastic convolutions withrespect to a strongly continuous map $R:(0,T]\rightarrow L(H)$, not necessarilya semigroup. We prove existence of predictable versions of stochasticconvolutions and we characterize the measurability needed by operator-valuedprocesses in order to be convoluted with $R$. Finally, when $R$ is a$C_0$-semigroup and the stochastic integral provides continuous paths, we showexistence of a continuous version of the convolution, by adapting thefactorization method to the present setting.

A note on stochastic Fubini's theorem and stochastic convolution