Related papers: Convolution type stochastic Volterra equations

The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…

The note is devoted to estimates for convolutions appearing in some class of stochastic Volterra equations. Two maximal inequalities and exponential tail estimate are proved by the fractional method of infinite dimensional stochastic…

The dynamics of a system of particles subject to a 4th order potential field modeling the space-time evolution of wedge disclinations is studied, focusing on finite systems of disclinations within a circular domain. Existence theorems for…

This paper provides a Feller's test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of…

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, the existence and…

We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar…

This paper is devoted to study a class of stochastic Volterra equations associated with fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct…

We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither…

Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for…

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…

Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear…

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…

Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional…

Stochastic Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural stochastic Volterra equations as a physics-inspired architecture,…

We prove strong existence and uniqueness, and H\"older regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an…

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…

We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued…

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space $L^p$. The corresponding regularity is obtained by showing that the stochastic convolution…

We study the class of continuous polynomial Volterra processes, which we define as solutions to stochastic Volterra equations driven by a continuous semimartingale with affine drift and quadratic diffusion matrix in the state of the…