Related papers: Stochastic equations of non-negative processes wit…

In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions to SDE's. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate Markov property. To…

This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…

We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence…

The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete,…

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We…

We present an It\^o formula for the $L_p$-norm of jump processes having stochastic differentials in $L_p$-spaces. The main results extend well-known theorems of Krylov to the case of processes with jumps, and which can be used to prove…

We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of…

In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. In particular a conditionally…

In this paper we establish the strong existence, pathwise uniqueness and a comparison theorem to a stochastic partial differential equation driven by Gaussian colored noise with non-Lipschitz drift, H\"older continuous diffusion…

We obtain sufficient condition for SDEs to evolve in the positive orthant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs…

We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show existence…

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous L\'evy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution.…

The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…

The object of the present paper is to find new sufficient conditions for the existence of unique strong solutions to a class of (time-inhomogeneous) stochastic differential equations with random, non-Lipschitzian coefficients. We give an…

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.

In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We…

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a L\'evy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying…

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric L\'evy white noise. We identify conditions for existence for these two kinds of solutions,…

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable…