Related papers: Cylindrical Martingale Problems Associated with L\…

Lattice birth-and-death Markov dynamics of particle systems with spins from the set of non-negative integers are constructed as unique solutions to certain stochastic equations. Pathwise uniqueness, strong existence, Markov property and…

Our main result is the martingale representations for Markov additive processes where the modulator is a Levy process. These processes have three parts: the modulator, the jumps of the ordinate triggered by the modulator, and the…

In this article, the existence of a unique solution in the variational approach of the stochastic evolution equation $$\dX(t) = F(X(t)) \dt + G(X(t)) \dL(t)$$ driven by a cylindrical L\'evy process $L$ is established. The coefficients $F$…

For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt…

This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped property. The main results are established (i) in a Markovian…

This paper constructs a class of martingale transforms based on L\'evy processes on Lie groups. From these, a natural class of bounded linear operators on the $L^p$-spaces of the group (with respect to Haar measure) for $1<p<\infty$, are…

We deal with reflected solutions of anticipated backward doubly stochastic differential equations (RABDSDEs) driven by Teugels martingales associated with L\'evy process under a Lipschitz generator where the coefficients of these BDSDEs…

Let $L$ be a L\'evy-type generator whose L\'evy measure is controlled from below by that of a non-degenerate $\alpha$-stable ($0<\alpha<2$) process. In this paper, we study the martingale problem for the operator $\mathcal{L}_{t}=L+K_{t}$,…

Stochastic fractionally dissipative quasi-geostrophic type equation on $R^d$ with a multiplicative Gaussian noise is considered. We prove the existence of a martingale solution. In the 2D sub-critical case we prove also the pathwise…

We study class of L\'{e}vy processes having distributions being indentifiable by moments. We define system of polynomial martingales \newline $\left\{ M_{n}(X_{t},t),\mathcal{F}_{\leq t}\right\} _{n\geq 1},$ where $% \mathcal{F}_{\leq t}$…

In this paper, we propose a new notion of Forward--Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward--backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the…

In this article we prove martingale type pointwise convergence theorems pertaining to tensor product splines defined on $d$-dimensional Euclidean space ($d$ is a positive integer), where conditional expectations are replaced by their…

Starting from the seventies mathematicians face the question whether a non-negative local martingale is a true or a strict local martingale. In this article we answer this question from a semimartingale perspective. We connect the…

The solution of Poisson's equation plays a key role in constructing the martingale through which sums of Markov correlated random variables can be analyzed. In this paper, we study two different representations for the solution in countable…

Suppose that $d\geq1$ and $\alpha\in (1, 2)$. Let $Y$ be a rotationally symmetric $\alpha$-stable process on $\R^d$ and $b$ a $\R^d$-valued measurable function on $\R^d$ belonging to a certain Kato class of $Y$. We show that $\rd X^b_t=\rd…

We provide a condition for f-ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift…

Sets of orthogonal martingales are importants because they can be used as stochastic integrators in a kind of chaotic representation property, see [20]. In this paper, we revisited the problem studied by W. Schoutens in [21], investigating…

This paper studies the three-dimensional stochastic chemotaxis-Navier-Stokes (SCNS) system subjected to a L\'{e}vy-type random external force in bounded domain. Up to now, the existing results concerning global solvability of SCNS system…

In this Note we consider a quadratic backward stochastic differential equation (BSDE) driven by a continuous martingale $M$ and whose generator is a deterministic function. We prove (in Theorem \ref{theorem:main}) that if $M$ is a strong…

We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…