Work

Limit theorems for stochastic Volterra processes

Year: 2026

Type: article

Abstract: We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit distributions and stationary processes, a law of large numbers including a convergence rate, and the central limit theorem for time averages of the process within the Gaussian domain of attraction. As particular examples, we study Markovian lifts based on Laplace transforms in a weighted Hilbert space of densities and Markovian lifts based on the shift semigroup on the Filipović space. We illustrate our results for the case of fractional stochastic Volterra equations with additive or multiplicative Gaussian noise.

Source: Stochastic Partial Differential Equations Analysis and Computations

DOI: 10.1007/s40072-026-00428-w

Authors: Luigi Amedeo Bianchi, Stefano Bonaccorsi, Ole Cañadas, Martin Friesen

Institutions: University of Trento, Dublin City University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Irish Research Council, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, NextGenerationEU