On uniqueness for some non-Lipschitz SDE

On Uniqueness of"SDE Decomposition"in A-type Stochastic Integration

An innovative theoretical framework for stochastic dynamics based on a decomposition of a stochastic differential equation (SDE) has been developed with an evident advantage in connecting deterministic and stochastic dynamics, as well as useful applications in physics, engineering, chemistry and biology. It introduces the A-type stochastic integration for SDE beyond traditional Ito’s or Straton...

On Pathwise Uniqueness for Stochastic Heat Equations with Non-lipschitz Coefficients

Here denotes the Laplacian and Ẇ is space–time white noise on R+ ×R. It is known that uniqueness in law holds for solutions to (1) in the appropriate space of continuous functions and such solutions are the density for one-dimensional super-Brownian motion (see, e.g., Section III.4 of [4]). One motivation for studying pathwise uniqueness is the hope that such an approach would be more robust an...

Some Geometric Properties for a Class of Non-Lipschitz Domains

In this paper, we introduce a class C, of domains of RN , N ≥ 2, which satisfy a geometric property of the inward normal (such domains are not Lipschitz, in general). We begin by giving various results concerning this property, and we show the stability of the solution of the Dirichlet problem when the domain varies in C.

Existence and Uniqueness of Mild Solutions to Some Neutral Stochastic Partial Functional Integrodifferential Equations with Non-Lipschitz Coefficients

Existence-uniqueness for Stochastic Functional Differential Equations with Non-Lipschitz Coefficients

The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) with non-Lipschitz coefficients. Firstly, we show that Peano’s theorem holds for SFDEs, that is, the continuity alone is sufficient to prove the local existence of the initial value problem of SFDEs. Secondly, some new uniqueness theorems are established by the comparison methods...