The law of iterated logarithm for solution of stochastic equations with periodic coefficients
type: Item
instance of: scholarly article
title: The law of iterated logarithm for solution of stochastic equations with periodic coefficients
zbMATH Open document ID: 0879.60024
DOI: 10.1007/BF02308825
published in: Mathematical Notes
publication date: 1997-08-18T00:00:00Z
review text: The author considers the \(d\)-dimensional stochastic equation \[ \xi(t)=\int_0^tb(s,\xi(s)) ds+\int_0^t\sigma(s,\xi(s)) dw(s),\;\;t\geq 0, \] where \(w\) is an \(m\)-dimensional standard Wiener process and a \(d\)-dimensional vector function \(b\) and a \(d\times m\)-matrix function are periodic functions with respect to each of the variables. It is proved under appropriate conditions that \[ P\Biggl\{\limsup_{t\to\infty}{\xi_i(t)-\lambda_it\over \sqrt{2H_it\ln\ln t}}=1 \Biggr\}=1,\quad P\Biggl\{\liminf_{t\to\infty}{\xi_i(t)-\lambda_it\over \sqrt{2H_it\ln\ln t}}=-1 \Biggr\}=1,\quad i=1,...,d, \] with the same numbers \(H_i,\lambda_i\).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1037763
zbMATH Keywords: stochastic equation
zbMATH Keywords: iterated logarithm for solutions
author: S. Ya. Makhno
reviewed by: A. Ya. Dorogovtsev
MaRDI profile type: Publication
cites work: Q5341279
cites work: Q4189539
cites work: Q4118565
full work available at URL: https://doi.org/10.1007/bf02308825
OpenAlex ID: W2123287695
description: scientific article; zbMATH DE number 1037763