We consider the weakly damped stochastic nonlinear Schr\"odinger (NLS) equation on the real line, driven by a noise that is white in time and smooth in space. Assuming that the noise is sufficiently non-degenerate, we prove that the equation has a unique stationary measure in the class of probability measures concentra...
For a stochastic partial differential equation posed on a Gelfand triple and satisfying the fully local monotone conditions of R\"ockner, Shang and Zhang, we compute the logarithmic derivative of the law of the solution at a fixed time along a prescribed direction of the state space. The formula is intrinsic, being exp...
Ehsan Mirafzali, F. Proske, Razvan Marinescu· 0 citations
In this paper, we establish large deviations of invariant measures for fractional stochastic reaction-diffusion equations with polynomial reaction term driven by unbounded multiplicative noise on R^n. Under a dissipativity condition, we first prove the Freidlin-Wentzell large deviation principle of solution trajectorie...
We develop a rigorous analytical framework for Riemann-Liouville fractional
stochastic differential equations (RL-FSDEs), addressing a gap in the literature where existing treatments either focus on Caputo formulations or
provide incomplete existence arguments. Our approach combines Laplace transform operational calc...
Mohsen Alhassoun, Khalil Yahya, A. Abdallah· Boletim da Sociedade Paranae...· 0 citations
This paper studies fundamental solutions of uniformly parabolic systems with stationary random coefficients depending on space and time. Under ergodicity and local regularity, we establish quenched Gaussian bounds for the kernel and its spatial derivatives, with stationary random prefactors. A spectral gap assumption g...
For weak solutions to quasilinear degenerate parabolic equations of $p$-Laplace type, a central obstacle in applying the method of intrinsic scaling to prove their H\"{o}lder regularity is the derivation of forward-in-time propagation estimate for the spatial measure of level sets. In this paper, we revisit and overcom...
Xia Hao, Yan Li, Zhi-Wen Zhao· 0 citations
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