Stochastics Seminar

Speaker: Dr. Erkan Nane

Topic:  Intermittence and  time fractional stochastic partial differential equations

Abstract: In this talk, I consider time fractional stochastic heat type equations. The time fractional stochastic heat type equations might be used to model phenomenon with random effects with thermal memory. In this talk I discuss: (i) Existence and uniqueness of solutions and existence of a continuous version of the solution; (ii) absolute moments of the solutions of this equation grow exponentially; and (iii) the distances to the origin of the farthest high peaks of those moments grow exactly linearly with time.  These results extend the results of Mohammud Foondun and Davar Khoshnevisan, (Intermittence and nonlinear parabolic stochastic partial differential equations, Electron. J. Probab. 14 (2009), no. 21, 548--568) and Daniel Conus and Khoshnevisan (On the existence and position of the farthest peaks of a family of stochastic heat and wave equations, Probab. Theory Related Fields 152 (2012), no. 3-4, 681--701)  on the parabolic stochastic heat equations. --- This is a recent joint work with Jebessa B Mijena.