Related papers: On pathwise uniqueness for stochastic differential…

We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric $\alpha$-stable L\'evy processes with values in $\R^d$ having a bounded and $\beta$-H\"older continuous drift term. We assume $\beta > 1 -…

For $\alpha\in (0,1)$, we consider stochastic differential equations driven by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\] We prove that pathwise uniqueness holds for this equation under the assumptions that…

In this article we prove the pathwise uniqueness for stochastic differential equations in $\mR^d$ with time-dependent Sobolev drifts, and driven by symmetric $\alpha$-stable processes provided that $\alpha\in(1,2)$ and its spectral measure…

We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with H\"older continuous drift, thus obtaining an infinite dimensional generalization of the result of Priola…

We consider non-degenerate SDEs with a $\beta$-Holder continuous and bounded drift term and driven by a Levy noise $L$ which is of $\alpha$-stable type. If $\alpha \in [1,2)$ and $\beta \in (1 - \frac{\alpha}{2},1) $ we show pathwise…

Pathwise uniqueness for multi-dimensional stochastic McKean--Vlasov equation is established under moderate regularity conditions on the drift and diffusion coefficients. Both drift and diffusion depend on the marginal measure of the…

We consider one-dimensional stochastic differential equations with jumps in the general case. We introduce new technics based on local time and we prove new results on pathwise uniqueness and comparison theorems. Our approach are very easy…

We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise…

We obtain the unique weak and strong solvability for time inhomogeneous stochastic differential equations with the drift in subcritical Lebesgue--H\"{o}lder spaces $L^p([0,T];{\mathcal C}_b^{\beta}({\mathbb R}^d;{\mathbb R}^d))$ and driven…

We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation \[dX_t=|X_t|^{\alpha} dW_t,\] where $W_t$ is a one-dimensional Brownian motion and $\alpha\in(0,1/2)$. Weak…

This paper establishes a quantitative stability theory for one-dimensional stochastic differential equations (SDEs) with non-zero drift, driven by a symmetric $\alpha$-stable process for $\alpha\in(1,2)$. Our work generalizes the classical…

We prove that the stochastic differential equation $$ Y_{s,t}(x) = Y_{s,s}(x) + \int_0^{t-s} f(Y_{s,s+u}(x)) dX_{s+u}, Y_{s,s}(x)=x\in\R^d. $$ driven by a L\'evy process whose paths have finite p-variation almost surely for some $p\in[1,2)$…

For $\alpha \in (1,2)$, we study the following stochastic differential equation driven by a non-degenerate symmetric $\alpha$-stable process in $\mathbb{R}^d$: \begin{align*} {\rm d} X_t=b(t,X_t){\mathord{{\rm d}}}…

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,…

One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with…

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 study the stochastic transport equation with globally $\beta$-H\"older continuous and bounded vector field driven by a non-degenerate pure-jump L\'evy noise of $\alpha$-stable type. Whereas the deterministic transport equation may lack…

In this paper, we investigate stochastic differential equations(SDEs) driven by a class of supercritical $\alpha$-stable process(including the rotational symmetric $\alpha-$stable process) with drift $b$. The weak well-posedness is proved,…

We consider the stochastic differential equation $$ dX_t = b(X_t) dt + dL_t,$$ where the drift $b$ is a generalized function and $L$ is a symmetric one dimensional $\alpha$-stable L\'evy processes, $\alpha \in (1, 2)$. We define the notion…

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $\alpha$-stable processes (including cylindrical ones) with $\alpha \in (1,2)$. We first establish a quantitative estimate for the…