4 papers · 1 filter
The martingale representation theorem for cylindrical martingale valued measures
S. Cambronero, D. Campos, C. A. Fonseca-Mora +1
We prove a martingale representation theorem for cylindrical martingale-valued measures defined on a separable Banach space. The main tool for establishing the theorem, is a new th…
Itô's Formula for Itô processes defined with respect to a cylindrical-martingale valued measure
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
Using the authors' recently developed stochastic integration [Stoch PDE: Anal Comp, 2024], we prove an Itô formula for Hilbert space-valued Itô processes defined with respect to…
Markov property and path regularity for the solutions to SPDEs driven by cylindrical-martingale valued measures
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
In this paper we prove the Markov property for the solution to stochastic partial differential equations driven by a cylindrical orthogonal martingale-valued measure. We assume our…
Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
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 qua…