Related papers: Existence and uniqueness of solutions of stochasti…

In this paper, we study a class of stochastic differential equations with additive noise that contains a fractional Brownian motion (fBM) and a Poisson point process of class (QL). The differential equation of this kind is motivated by the…

We study strong existence and pathwise uniqueness for a class of infinite-dimensional singular stochastic differential equations (SDE), with state space as the cone $\{x \in \mathbb{R}^{\mathbb{N}}: -\infty < x_1 \leq x_2 \leq \cdots\}$,…

In this paper, we study some existence and uniqueness results for systems of differential equations in which each of equations of the system involves a different Stieltjes derivative. Specifically, we show that this problems can only have…

In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.

We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

We study existence and uniqueness for one-dimensional generalized stochastic differential equations with singular coefficients, including distributional drift and degenerate, possibly discontinuous, diffusion coefficients. Such…

This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…

We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with $\alpha\in(0,2]$, to include both linear multifractional Brownian sheets ($\alpha=2$) and linear multifractional stable sheets ($\alpha<2$). The…

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…

We prove the existence and the uniqueness of a solution to the stochastic NSLE on a two-dimensional compact riemannian manifold. Thus we generalize a recent work by Burq, G\'erard and Tzvetkov in the deterministic setting, and a series of…

This paper deals with initial value problems for fractional functional differential equations with bounded delay. The fractional derivative is defined in the Caputo sense. By using the Schauder fixed point theorem and the properties of the…

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases.…

In this paper we present a new method for the construction of strong solutions of SDE's with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter H < 1/2. Furthermore, we prove…

We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…

In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type…

We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional…

We show the existence and uniqueness of strong solutions for stochastic differential equation driven by partial $\alpha$-stable noise and partial Brownian noise with singular coefficients. The proof is based on the regularity of degenerate…

In two preceding articles, we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift $f(b,x,z)$. The purpose of this…

In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the…