ERA

Download the full-sized PDF of A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameterDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R3KK4H

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Mathematical and Statistical Sciences, Department of

Collections

This file is in the following collections:

Research Publications (Mathematical and Statistical Sciences)

A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter Open Access

Descriptions

Author or creator
Kouritzin, Michael
Heunis, A.J.
Additional contributors
Subject/Keyword
mixing processes
ordinary differential equation
laws of the iterated logarithm
central limit theorem
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
Consider the following random ordinary differential equation: X˙ϵ(τ)=F(Xϵ(τ),τ/ϵ,ω)subject toXϵ(0)=x0, where {F(x,t,ω),t≥0} are stochastic processes indexed by x in Rd, and the dependence on x is sufficiently regular to ensure that the equation has a unique solution Xϵ(τ,ω) over the interval 0≤τ≤1 for each ϵ>0. Under rather general conditions one can associate with the preceding equation a nonrandom averaged equation: x˙0(τ)=F¯¯¯(x0(τ))subject tox0(0)=x0, such that limϵ→0sup0≤τ≤1E|Xϵ(τ)−x0(τ)|=0. In this article we show that as ϵ→0 the random function (Xϵ(⋅)−x0(⋅))/2ϵloglogϵ−1−−−−−−−−−−√ almost surely converges to and clusters throughout a compact set K of C[0,1].
Date created
1994
DOI
doi:10.7939/R3KK4H
License information
Creative Commons Attribution-Non-Commercial-No Derivatives 3.0 Unported
Rights

Citation for previous publication
M.A. Kouritzin and A.J. Heunis, "A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter'', Annals of Probability, 22(2) (1994) pp. 659-679.
Source
Link to related item

File Details

Date Uploaded
Date Modified
2014-05-01T01:10:42.635+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 3615874
Last modified: 2015:10:12 13:40:50-06:00
Filename: AP_1994_22_2_659.pdf
Original checksum: fdbb122896749adb8a3749a95847b835
Well formed: true
Valid: true
Page count: 21
File language: en-US
Activity of users you follow
User Activity Date