Donskerâs Delta Functional of Stochastic Processes with Memory

Herry Pribawanto Suryawan

doi:10.5614/j.math.fund.sci.2019.51.3.5

Authors

Herry Pribawanto Suryawan Department of Mathematics, Faculty of Science and Technology Sanata Dharma University, Jalan Affandi, Catur Tunggal, Yogyakarta 552821

DOI:

https://doi.org/10.5614/j.math.fund.sci.2019.51.3.5

Keywords:

Donsker delta functional, Hida calculus, local time, stochastic process with memory, white noise

Abstract

A class of stochastic processes with memory within the framework of the Hida calculus was studied. It was proved that the Donsker delta functionals of the processes are Hida distributions. Furthermore, the probability density function of the processes and the chaos decomposition of the Donsker delta functional were derived. As an application, the existence of the renormalized local times in an arbitrary dimension of the Riemann-Liouville fractional Brownian motion as a white noise generalized function was proved.

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