We study stochastic Volterra equations in Hilbert spaces driven by cylindrical Gaussian noise. We derive a mild formulation for the stochastic Volterra equation, prove the equivalence of mild and strong solutions, and study the existence and uniqueness of mild solutions. We also study space-time regularity. Furthermore, we establish the stability of mild solutions in $L^q(R_+)$, prove the existence of limit distributions in the Wasserstein p-distance with $p\in [1,\infty)$, and characterise when these limit distributions are independent of the initial state of the process despite the presence of memory. While our techniques allow for a general class of Volterra kernels, they are particularly suited for completely monotone kernels and fractional Riemann-Liouville kernels in the full range $\alpha\in(0,2)$.

Limits of stochastic Volterra equations driven by Gaussian noise / Bianchi, Luigi Amedeo; Bonaccorsi, Stefano; Friesen, Martin. - In: STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS: ANALYSIS AND COMPUTATIONS. - ISSN 2194-0401. - 2024:(2024). [10.1007/s40072-024-00340-1]

Limits of stochastic Volterra equations driven by Gaussian noise

Bianchi, Luigi Amedeo;Bonaccorsi, Stefano;
2024-01-01

Abstract

We study stochastic Volterra equations in Hilbert spaces driven by cylindrical Gaussian noise. We derive a mild formulation for the stochastic Volterra equation, prove the equivalence of mild and strong solutions, and study the existence and uniqueness of mild solutions. We also study space-time regularity. Furthermore, we establish the stability of mild solutions in $L^q(R_+)$, prove the existence of limit distributions in the Wasserstein p-distance with $p\in [1,\infty)$, and characterise when these limit distributions are independent of the initial state of the process despite the presence of memory. While our techniques allow for a general class of Volterra kernels, they are particularly suited for completely monotone kernels and fractional Riemann-Liouville kernels in the full range $\alpha\in(0,2)$.
2024
Bianchi, Luigi Amedeo; Bonaccorsi, Stefano; Friesen, Martin
Limits of stochastic Volterra equations driven by Gaussian noise / Bianchi, Luigi Amedeo; Bonaccorsi, Stefano; Friesen, Martin. - In: STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS: ANALYSIS AND COMPUTATIONS. - ISSN 2194-0401. - 2024:(2024). [10.1007/s40072-024-00340-1]
File in questo prodotto:
File Dimensione Formato  
document.pdf

Solo gestori archivio

Descrizione: online first
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 621.45 kB
Formato Adobe PDF
621.45 kB Adobe PDF   Visualizza/Apri
Limits_of_stochastic_Volterra_equations_driven_by_gaussian_noise-1.pdf

embargo fino al 02/11/2025

Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 534.25 kB
Formato Adobe PDF
534.25 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/437846
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
  • OpenAlex ND
social impact