C. Fonseca-Mora

activity

20152026

most citedStochastic Integration and Stochastic PDEs Driven by Jumps on the Dual of a Nuclear Space

13 citations · 55 across the 19 of their papers we have counts for

collaborators

20 papers

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…

math.PR2025

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…

math.PR2024

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 a…

math.PR2023

Tightness and weak convergence in the topology of local uniform convergence for stochastic processes in the dual of a nuclear space

C. A. Fonseca-Mora

Let $Φ^{'}$ denote the strong dual of a nuclear space $Φ$ and let $C_{\infty} (Φ^{'})$ be the collection of all continuous mappings $x : [0, \infty) \to Φ^{'}$ equipped with the topolog…

math.FA2023

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…

math.PR2023

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…

math.PR2023★ 1 cited

Convergence Uniform on Compacts in Probability with Applications to Stochastic Analysis in Duals of Nuclear Spaces

C. A. Fonseca-Mora

Let $Φ^{'}$ denote the strong dual of a nuclear space $Φ$ . In this paper we introduce sufficient conditions for the convergence uniform on compacts in probability for a sequence of $Φ…

math.PR2022★ 1 cited

Time regularity of stochastic convolutions and stochastic evolution equations in duals of nuclear spaces

C. A. Fonseca-Mora

Let $Φ$ a locally convex space and $Ψ$ be a quasi-complete, bornological, nuclear space (like spaces of smooth functions and distributions) with dual spaces $Φ^{'}$ and $Ψ^{'}$ . In this…

math.PR2022★ 1 cited

Almost Sure Uniform Convergence of Stochastic Processes in the Dual of a Nuclear Space

C. A. Fonseca-Mora

Let $Φ$ be a nuclear space and let $Φ^{'}$ denote its strong dual. In this paper we introduce sufficient conditions for the almost surely uniform convergence on bounded intervals of t…

math.PR2021★ 2 cited

Stochastic Evolution Equations with Lévy Noise in the Dual of a Nuclear Space

C. A. Fonseca-Mora

In this article we give sufficient and necessary conditions for the existence of a weak and mild solution to stochastic evolution equations with (general) Lévy noise taking values…

math.PR2020★ 2 cited

Stochastic integration with respect to cylindrical semimartingales

C. A. Fonseca-Mora

In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space $Φ$ . Our construction of the stoc…

math.PR2020★ 4 cited

Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures

A. E. Alvarado-Solano, C. A. Fonseca-Mora

In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces…

math.PR2019★ 2 cited

Regularization of Cylindrical Processes In Locally Convex Spaces

C. A. Fonseca-Mora

Let $Φ$ be a locally convex space and let $Φ^{'}$ denote its strong dual. In this paper we introduce sufficient conditions for the existence of a continuous or a càdlàg $Φ^{'}$ -valued ve…

math.PR2019★ 4 cited

Semimartingales on Duals of Nuclear Spaces

C. A. Fonseca-Mora

This work is devoted to the study of semimartingales on the dual of a general nuclear space. We start by establishing conditions for a cylindrical semimartingale in the strong dual…

math.PR2018★ 5 cited

Tightness and Weak Convergence of Probabilities on the Skorokhod Space on the Dual of a Nuclear Space and Applications

C. A. Fonseca-Mora

Let $Φ_{β}^{'}$ denotes the strong dual of a nuclear space $Φ$ and let $D_{T} (Φ_{β}^{'})$ be the Skorokhod space of right-continuous with left limits (càdlàg) functions from $[0, T]$ into $Φ'…

math.PR2017★ 13 cited

Stochastic Integration and Stochastic PDEs Driven by Jumps on the Dual of a Nuclear Space

C. A. Fonseca-Mora

We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space. This is applied to deve…

math.PR2017★ 8 cited

Lévy Processes and Infinitely Divisible Measures in the Dual of a Nuclear Space

C. A. Fonseca-Mora

Let $Φ$ be a nuclear space and let $Φ_{β}^{'}$ denote its strong dual. In this work we establish the one-to-one correspondence between infinitely divisible measures on $Φ_{β}^{'}$ and Lévy p…

math.PR2015★ 12 cited

Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space

Christian Fonseca-Mora

Let $Φ$ be a nuclear space and let $Φ_{β}^{'}$ denote its strong dual. In this paper we introduce sufficient conditions for a cylindrical process in $Φ^{'}$ to have a version that is a $Φ'…