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We prove the existence and uniqueness of solution to obstacle problem for quasilinear stochastic partial differential equations with Neumann boundary condition. Our method is based on the analytical techniques coming from parabolic potential theory. The solution is expressed as a pair (u , ν) where u is a predictable continuous process which takes values in a proper Sobolev space and ν is a random regular measure satisfying minimal Skohorod condition. [ABSTRACT FROM AUTHOR]

By means of Itô's formula and a comparison theorem for integral equations, we study the blow up in finite time of semilinear stochastic differential equations of the form Here, is non-negative and non-decreasing by components, is a predictable and continuous process, is an -Brownian motion and is an -measurable random variable. The results of this paper can be seen as extensions of the Feller and Osgood criteria. [ABSTRACT FROM AUTHOR]

We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (in short OSPDE) under a weaker integrability condition on the coefficient and the barrier. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to establish a new LaSalle-type theorem for stochastic differential delay equations of neutral type. From the theorem follow some useful criteria on the orbital asymptotic stability. Several examples are also given for illustration. This shows clearly the power of our new theorem. [ABSTRACT FROM AUTHOR]

In this paper we review our recent research on stochastic delay population dynamics. The main aim is to reveal that a different type of environmental noise has a different effect on delay population systems. [ABSTRACT FROM AUTHOR]