7 papers
Itô's formula for Lévy-Itô processes taking values in the dual of nuclear space
C. A. Fonseca-Mora
Using the theory of stochastic integration in duals of nuclear spaces with respect to cylindrical martingale-valued measures, a vector-valued Itô formula is proved for generalized…
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…
Vector-Valued Stochastic Integration With Respect to Semimartingales in the Dual of Nuclear Space
C. A. Fonseca-Mora
In this work, we investigate a theory of stochastic integration for operator-valued processes with respect to semimartingales taking values in the dual of a nuclear space. Our cons…
Riesz spaces of signed charges on semi-rings
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
A constructive definition of the supremum of a family of set functions is exploited in the context of Riesz spaces of signed measures and finitely additive functions (signed charge…