Abstract We consider stochastic differential equations of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$ , where f ( x ) behaves comparably to $|x|^k$ in a neighborhood origin, for $k\in [1,\infty)$ . show that there exists threshold value $ \,{:}\,{\raise-1.5pt{=}}\, \tilde{\gamma}$ $\gamma$ depending on k such if $\gamma \in (1/2, \tilde{\gamma})$ then $\mathbb{P}(X_t\rightarrow 0...

The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in smooth bounded domain \begin{document}$ \mathbb{R}^{3} $\end{document} with large initial data. The coupled structure makes the a...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

We extend the traditional two-stage linear stochastic program by probabilistic constraints imposed in the second stage. This adds nonlinearity such that basic arguments for analyzing the structure of linear two-stage stochastic programs have to be rethought from the very beginning. We identify assumptions under which the problem is structurally sound and behaves stable under perturbations of pr...