Paper ID: 8534

Donsker’s Delta Functional of Stochastic Processes with Memory

Herry Pribawanto Suryawan

Department of Mathematics, Sanata Dharma University, Yogyakarta, Indonesia

Abstract. We study a class of stochastic processes with memory within the framework of Hida calculus. We show that the Donsker delta functionals of the processes are Hida distributions. Furthermore, we derive the probability density function of the process and the chaos decomposition of the Donsker delta functional. As an application we prove the existence of the renormalized local times in arbitrary dimension of the Riemann-Liouville fractional Brownian motion as white noise generalized function.

Keywords: Donsker’s delta functional; Hida calculus; Stochastic process with memory

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