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All Journal Journal of the Indonesian Mathematical Society Journal of Mathematical and Fundamental Sciences BAREKENG: Jurnal Ilmu Matematika dan Terapan Limits: Journal of Mathematics and Its Applications Pattimura Proceeding : Conference of Science and Technology
Herry Pribawanto Suryawan
Sanata Dharma University
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A WHITE NOISE APPROACH TO THE SELF-INTERSECTION LOCAL TIMES OF A GAUSSIAN PROCESS Suryawan, Herry Pribawanto
Journal of the Indonesian Mathematical Society Volume 20 Number 2 (October 2014)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.20.2.136.111-124

Abstract

In this paper we show that for any spatial dimension the renormalized self-intersection local times of a certain Gaussian process defined by indefinite Wiener integral exist as Hida distributions. An explicit expression for the chaos decomposition in terms of Wick tensor powers of white noise is also obtained. We also study a regularization of the self-intersection local times and prove a convergence result in the space of Hida distributions.DOI : http://dx.doi.org/10.22342/jims.20.2.136.111-124
A WHITE NOISE APPROACH TO THE SELF-INTERSECTION LOCAL TIMES OF A GAUSSIAN PROCESS Herry Pribawanto Suryawan
Journal of the Indonesian Mathematical Society Volume 20 Number 2 (October 2014)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.20.2.136.111-124

Abstract

In this paper we show that for any spatial dimension the renormalized self-intersection local times of a certain Gaussian process defined by indefinite Wiener integral exist as Hida distributions. An explicit expression for the chaos decomposition in terms of Wick tensor powers of white noise is also obtained. We also study a regularization of the self-intersection local times and prove a convergence result in the space of Hida distributions.DOI : http://dx.doi.org/10.22342/jims.20.2.136.111-124
Donsker’s Delta Functional of Stochastic Processes with Memory Herry Pribawanto Suryawan
Journal of Mathematical and Fundamental Sciences Vol. 51 No. 3 (2019)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2019.51.3.5

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.
Pendekatan Analisis Derau Putih untuk Arus Stokastik dari Gerak Brown Subfraksional Herry Pribawanto Suryawan
Limits: Journal of Mathematics and Its Applications Vol 19, No 1 (2022)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v19i1.8974

Abstract

The subfractional Brownian motion is a Gaussian generalization of the Brownian motion whose increments are not stationary. In this paper we study the stochastic current of the one dimensional subfractional Brownian motion. For this purpose we use the method from white noise analysis by representing the subfractional Brownian motion as stochastic functionals of white noise.  As the main result we prove that the stochastic current of the one dimensional subfractional Brownian motion is a generalized function in the space of Hida distributions.
SOME BASIC PROPERTIES OF THE NOISE REINFORCED BROWNIAN MOTION Herry Pribawanto Suryawan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (409.879 KB) | DOI: 10.30598/barekengvol16iss2pp363-370

Abstract

Noise reinforced Brownian motion appears as the universal limit of the step reinforced random walk. This article aims to study some basic properties of the noise reinforced Brownian motion. As main results, we prove integral representation, series expansion, Markov property, and martingale property of the noise reinforced Brownian motion.
PENDEKATAN KALKULUS HIDA UNTUK PROSES HERMITE Herry Pribawanto Suryawan
Pattimura Proceeding 2021: Prosiding KNM XX
Publisher : Pattimura University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1731.893 KB) | DOI: 10.30598/PattimuraSci.2021.KNMXX.91-98

Abstract

Proses Hermite order k didefinisikan melalui integral lipat Wiener-Itˆo order k terhadapgerakBrownbaku. ProsesHermiteorder1tidaklainadalahgerakBrownfraksionaldan merupakansatu-satunyaprosesHermiteyangmempunyaisifatGaussian. Sementaraituproses Hermite order 2 dikenal dengan nama proses Rosenblatt. Pada makalah ini kita akan membahas proses Hermite dengan menggunakan kalkulus Hida, yakni proses Hermite direpresentasikan sebagai fungsi yang diperumum stokastik dengan peubah acak dasar yang digunakan adalah derau putih Brownian. Sebagai hasil utama akan ditunjukkan bahwa proses Hermite terdiferensial di dalam ruang distribusi Hida dan juga diperoleh sebuah rumus eksplisit untuk derau Hermite
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