arXiv subjects

Santiago Cambronero

Publications and source records attributed to Santiago Cambronero.

5 recordsLinked to original sources

arXiv2026

Itô's Formula for Itô processes defined with respect to a cylindrical-martingale valued measure

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 cylindrical martingale-valued measure. We develop some tools from stochastic analysis, as are the predictable and optional quadratic variation of a stochastic integral, the continuous and purely discontinuous parts of an integral process, and a Riemann representation formula. As an application of our Itô formula, we prove a Burkholder inequality for the stochastic integral defined with respect to a cylindrical martingale-valued measure. Finally, we derive Itô formulas for Hilbert space-valued martingale-valued measures and for cylindrical square integrable martingales.

math.PR↗

arXiv2026

Markov property and path regularity for the solutions to SPDEs driven by cylindrical-martingale valued measures

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 coefficients are time-dependent and satisfy some growth and Lipschitz conditions. We also prove that for time-independent coefficients and under mild assumptions on the cylindrical orthogonal martingale-valued measure, the solutions to our stochastic partial differential equations are Feller. Finally, in the case that the $C_{0}$-semigroup is quasi-contraction, we show that the solution to our stochastic partial differential equation possesses a càdlàg version.

math.PR↗

arXiv2024

Riesz spaces of signed charges on semi-rings

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 charges) on semi-rings. We explore applications, particularly to establish a Jordan decomposition for signed charges on semi-rings, whether the structure of Riesz space is present or not.

math.FA↗

arXiv2024

Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs

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.

math.PR↗

arXiv2006

On the shape of the ground state eigenvalue density of a random Hill's equation

Consider the Hill's operator $Q = - d^2/dx^2 + q(x)$ in which $q(x)$, $0 \le x \le 1$, is a White Noise. Denote by $f(μ)$ the probability density function of $-λ_0(q)$, the negative of the ground state eigenvalue, at $μ$. We describe the detailed asymptotics of this density as $μ\to +\infty$. This result is based on a precise Laplace analysis of a functional integral representation for $f(μ)$ established by S. Cambronero and H.P. McKean.

math.PR↗