Large Deviations for Stochastic Volterra Equations (original) (raw)

Stochastic Volterra equations under perturbations

Electronic Communications in Probability, 2014

We study stochastic perturbed Volterra equations of convolution type in an infinite dimensional case. Our interest is directed towards the existence and regularity of stochastic convolutions connected to the equations considered under some kind of perturbations. We use an operator theoretical method for the representation of solutions.

Strong solutions to stochastic Volterra equations

2005

In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties for stochastic convolutions are studied. Our main result provide sufficient conditions for strong solutions to stochastic Volterra equations.

Comparison of Stochastic Volterra Equations

Bernoulli, 2000

A pathwise comparison theorem for a class of one-dimensional stochastic Volterra equations driven by continuous semimartingales is proved under suitable conditions. The result is applied to equations appearing in applications.

On numerical solutions to stochastic Volterra equations

2004

In the first part we recall some apparently well-known results concerning the Volterra equations under consideration. In the second one we describe a numerical algorithm used and next present some examples of numerical solutions in order to illustrate the pertinent features of the technique used in the paper.

Stochastic Volterra equations of nonscalar type

2005

In the paper stochastic Volterra equations of nonscalar type are studied using resolvent approach. The aim of this note is to provide some results on stochastic convolution and integral mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials.

Large deviations for a stochastic Volterra-type equation in the Besov–Orlicz space

Stochastic Processes and their Applications, 1999

In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov-Orlicz space B 0 ; ! modulated by the Young function (t) = exp(t 2 ) − 1 and the modulus of continuity !(t) = (t(1 + log(1=t))) 1=2 . Moreover, we derive in the Besov-Orlicz norm a large deviation estimate of Freidlin-Wentzell type for the solution.

Some results on stochastic convolutions arising in Volterra equations perturbed by noise

Analisi matematica.-Some results on stochastic convolutions arising in Volterra equations perturbed by noise. Nota di PHILIPPE CLéMENT e GIUSEPPE DA PRATO, presentata!") dal Corrisp. G. Da Prato. ABSTRACT.-Regularity of stochastic convolutions corresponding to a Volterra equation, perturbed by a white noise, is studied. Under suitable assumptions, hòlderianity of the corresponding trajectories is proved. KEY WORDS: Stochastic convolution; Volterra equations; Completely positive kernels. RIASSUNTO.-Sulle convoluzioni stocastiche relative a equazioni di Volterra perturbate da un rumore. Si dimostra la regolarità della convoluzione stocastica relativa a equazioni di Volterra perturbate da un rumore bianco. Sotto opportune ipotesi viene provata l'hòlderianità delle traiettorie corrispondenti.

On numerical solutions to stochastic Volterra equations 1

2004

The aim of the paper is to demonstrate the use of the Galerkin method for some kind of Volterra equations, determininistic and stochastic as well. The paper consists of two parts: the theoretical and numerical one. In the first part we recall some apparently well-known results concerning the Volterra equations under consideration. In the second one we describe a numerical algorithm used and next present some examples of numerical solutions in order to illustrate the pertinent features of the technique used in the paper.

Regularity of solutions to stochastic Volterra equations of convolution type

Integral Transforms and Special Functions, 2009

In this article we give necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a d-dimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used. The work applies to both the stochastic heat and wave equations.

Temporal and spatial regularity of solutions to stochastic Volterra equations of convolution type

In the paper regularity of solutions to stochastic Volterra equations in a separable Hilbert space is studied. Sufficient conditions for the temporal and spatial regularity of stochastic convolutions corresponding to the equations under consideration are provided. The results obtained generalize some well-known regularity results for solutions to stochastic differential equations. The paper is a continuation of previous author's papers concerning stochastic Volterra equations.