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math.PR2026
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…
math.PR2026
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…
math.PR2026
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…