Gauss-Markov processes on Hilbert spaces

2013/07/10 by Beniamin Gołdys, Goldys, Ben, Szymon Peszat +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G15 #60H15 #60J99 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1307.2686

openalex publication_date 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

K. Itô characterised in \citeito zero-mean stationary Gauss Markov-processes evolving on a class of infinite-dimensional spaces. In this work we extend the work of Itô in the case of Hilbert spaces: Gauss-Markov families that are time-homogenous are identified as solutions to linear stochastic differential equations with singular coefficients. Choosing an appropriate locally convex topology on the space of weakly sequentially continuous functions we also characterize the transition semigroup, the generator and its core thus providing an infinite-dimensional extension of the classical result of Courrège \citecourrege in the case of Gauss-Markov semigroups.

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