6 papers
Modulation and amplitude equations on bounded domains for nonlinear SPDEs driven by cylindrical α-stable Lévy processes
Shenglan Yuan, Dirk Blömker
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical α-stable Lévy processes via modulation or amp…
Stochastic turbulence for Burgers equation driven by cylindrical Lévy process
Shenglan Yuan, Dirk Blömker, Jinqiao Duan
This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodi…
Stochastic Bifurcation in Single-Species Model Induced by α-Stable Levy Noise
Almaz Tesfay, Daniel Tesfay, Shenglan Yuan +2
Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bif…
Action functionals for stochastic differential equations with Lévy noise
Shenglan Yuan, Jinqiao Duan
By using large deviation theory that deals with the decay of probabilities of rare events on an exponential scale, we study the longtime behaviors and establish action functionals…
Slow manifolds for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise
Hina Zulfiqar, Shenglan Yuan, Ziying He +1
This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking prop…
Characterization of the Most Probable Transition Paths of Stochastic Dynamical Systems with Stable Lévy Noise
Yuanfei Huang, Ying Chao, Shenglan Yuan +1
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric -stable Lévy motion () or Brown…