Related papers: An Operator Ito Formula for Volterra Gaussian Proc…

In this paper we obtain an It\^o differential representation for a class of singular stochastic Volterra integral equations. As an application, we investigate the rate of convergence in the small time central limit theorem for the solution.

In this paper we study dynamic backward problems, with the computation of conditional expectations as a main objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a…

We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is…

In this paper, we study the stabilization problem for the Ito systems with both multiplicative noise and multiple delays which exist widely in applications such as networked control systems. Sufficient and necessary conditions are obtained…

In this paper we provide a far-reaching generalization of the existent results about invariant subspaces of the differentiation operator $D=\frac{\partial}{\partial t}$ on $C^\infty(0,1)$ and the Volterra operator $Vf(t)=\int_0^tf(s)ds$, on…

In the framework of Soft de Sitter Effective Theory (SdSET), the Fokker-Planck equation for the late-time dynamics of the massless minimally coupled scalar field and its extension to the Kramers-Moyal equation are obtained from operator…

We consider a sequence of fractional Ornstein-Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of…

The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretisation, the basic problem can be represented as a matrix-vector…

Let $X$ be a (two-sided) fractional Brownian motion of Hurst parameter $H\in (0,1)$ and let $Y$ be a standard Brownian motion independent of $X$. Fractional Brownian motion in Brownian motion time (of index $H$), recently studied in…

We consider the regularity of sample paths of Volterra processes. These processes are defined as stochastic integrals $$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, $$ where $X$ is a semimartingale and $F$ is a deterministic…

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic…

We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an inhomogeneous kernel $K(t,s)$ and inhomogeneous drift and…

We calculate exactly the quantum mechanical, temporal characteristic function $\chi(\eta)$ for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. Knowledge of…

We study a compound Poisson (random time-change) approximation for stochastic differential equations (SDEs) and stochastic Volterra equations whose coefficients may be merely measurable in time and may even exhibit integrable singularities.…

We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…

We present an implementation of a fully self-consistent finite temperature second order Green's function perturbation theory (GF2) within the diagrammatic Monte Carlo framework. In contrast to the previous implementations of stochastic GF2…

This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estimate for the exact solution via analyzing the associated…

The van de Vusse reactor is an appealing benchmark problem in industrial control, since it has a non-minimum phase response. The van de Vusse stochasticity is attributed to the fluctuating input flow rate. The novelties of the paper are…

We present the novel Tensorized Discontinuous Isogeometric Analysis (TDIGA) method applied to the discontinuous Galerkin (DG) time-independent 2-D linearized Boltzmann transport equation (LBTE) with higher-order scattering, discretized with…

This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…