Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs

Fuente: arXiv
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Autori principali: Cambronero, Santiago, Campos, David, Fonseca-Mora, C. A., Mena, Darío
Natura: Preprint
Pubblicazione: 2023
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author Cambronero, Santiago
Campos, David
Fonseca-Mora, C. A.
Mena, Darío
author_facet Cambronero, Santiago
Campos, David
Fonseca-Mora, C. A.
Mena, Darío
contents We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the case of cylindrical martingale-valued measures that are allowed to have discontinuous paths (this is carried out within the context of separable Banach spaces). Our theory of stochastic integration is applied to address the existence and uniqueness of solutions to stochastic partial differential equations in Hilbert spaces.
format Preprint
id arxiv_https___arxiv_org_abs_2308_10374
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
Cambronero, Santiago
Campos, David
Fonseca-Mora, C. A.
Mena, Darío
Probability
Functional Analysis
60H05, 60H15, 60B11, 60G48
We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the case of cylindrical martingale-valued measures that are allowed to have discontinuous paths (this is carried out within the context of separable Banach spaces). Our theory of stochastic integration is applied to address the existence and uniqueness of solutions to stochastic partial differential equations in Hilbert spaces.
title Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
topic Probability
Functional Analysis
60H05, 60H15, 60B11, 60G48
url https://arxiv.org/abs/2308.10374