相关论文: Stochastic Volterra convolution with L\'evy proces…

We establish the first existence and uniqueness result for mild solutions of abstract stochastic evolution equations driven by arbitrary cylindrical L\'evy processes in Hilbert spaces. The coefficients are assumed to satisfy global…

This paper is concerned with the evolution dynamics of local times of a spectrally positive stable process in the spatial direction. The main results state that conditioned on the finiteness of the first time at which the local time at zero…

The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{\"o}lder continuous diffusion coefficients and sufficiently regular kernels. Moreover, we study the…

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy…

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 consider convolution-type stochastic Volterra equations with additive Hilbert-valued fractional Brownian motion, $0<H<1$. We find the weak solution to this stochastic Volterra equation, and study its stochastic integral part, the…

To describe stochastic quantum processes I propose an integral equation of Volterra type which is not generally transformable to any differential one. The process is a composition of ordinary quantum evolution which admits presence of a…

In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution…

The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We…

A stochastic process with movement, return, and rest phases is considered in this paper. For the movement phase, the particles move following the dynamics of Gaussian process or ballistic type of L\'evy walk, and the time of each movement…

In this paper we present some limit theorems for power variation of L\'evy semi-stationary processes in the setting of infill asymptotics. L\'evy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving…

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…

In this paper, we solve exit problems for a level-dependent L\'evy process which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All…

This note aims to give an explicit solution for backward stochastic Volterra integral equations with linear time delayed generators. The process $Y$ is expressed by an integral whose kernel is explicitly given. The processes $Z$ is…

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…

We consider a L\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample…

In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking the discrete convolution with respect to space variable in the system of fractional differential equations that governs its state…

This paper deals with generalized backward doubly stochastic differential equations driven by a L\'evy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp.…

In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…

We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…