Journal of Mathematical and Fundamental Sciences
Vol. 51 No. 3 (2019)

Donsker’s Delta Functional of Stochastic Processes with Memory

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

Article Info

Publish Date
31 Dec 2019

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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Journal Info
Journal of Mathematical and Fundamental Sciences
Website

Abbrev

jmfs

Publisher

Institut Teknologi Bandung

Subject

Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

Description

Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, ...