相关论文: Yamada-Watanabe uniqueness results for SPDEs drive…

We prove a dual Yamada-Watanabe theorem for one-dimensional stochastic differential equations driven by quasi-left continuous semimartingales with independent increments. In particular, our result covers stochastic differential equations…

We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear…

Based on the weak existence and weak uniqueness, we study the pathwise uniqueness of the solutions for a class of one-dimensional stochastic differential equations driven by pure jump processes. By using Tanaka's formula and the local time…

Recently, Kurtz (2007, 2014) obtained a general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations covering also the case of stochastic differential…

We give a unified proof of the Yamada-Watanabe-Engelbert theorem for various notions of solutions for SPDEs in Banach spaces with cylindrical Wiener noise. We use Kurtz' generalization of the theorems of Yamada, Watanabe and Engelbert. In…

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type. The results are applied to stochastic equations driven by…

We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic case, we also obtain the existence of unique strong…

A stochastic partial differential equation (SPDE) is derived for super-Brownian motion regarded as a distribution function valued process. The strong uniqueness for the solution to this SPDE is obtained by an extended Yamada-Watanabe…

We extend the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.

In a recent paper by the first two named authors, existence of martingale solutions to a stochastic nonlinear Schr\"odinger equation driven by a L\'evy noise was proved. In this paper, we prove pathwise uniqueness, uniqueness in law and…

We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called "method of the moving frame" allows us to reduce the proof to the Yamada-Watanabe Theorem for…

We consider various approximation properties for systems driven by a Mc Kean-Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations…

A result of A.M. Davie [Int. Math. Res. Not. 2007] states that a multidimensional stochastic equation $dX_t = b(t, X_t)\,dt + dW_t$, $X_0=x$, driven by a Wiener process $W= (W_t)$ with a coefficient $b$ which is only bounded and measurable…

We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose nonlinear drift parts are sums of the sub-differential of a convex function and a bounded part. This…

We provide the dual result of the Yamada-Watanabe theorem for mild solutions to semilinear stochastic partial differential equations with path-dependent coefficients. An essential tool is the so-called "method of the moving frame", which…

We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These solutions are characterized by a parametrized Young measure…

We prove the existence of probabilistically strong solutions for large classes of possibly degenerate stochastic differential equations with locally Sobolev-regular coefficients, using the restricted Yamada-Watanabe theorem. Our approach…

We show pathwise uniqueness for a class of degenerate It\^{o}-SDE among all of its weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Consequently, by the Yamada-Watanabe Theorem and a weak existence…

We establish existence of probabilistically strong solutions and pathwise uniqueness for a class of quasilinear stochastic evolution equations on bounded domains. Our results combine recent weak existence results for quasilinear stochastic…

In this work, we investigate the well-posedness of a stochastic heat equation with an arbitrary (but polynomial) nonlinearity in any dimension $d\geq 1$ perturbed by a multiplicative white noise in the Stratonovich form, subject to an…