scholarly journals On the Spitzer and Chung laws of the iterated logarithm for Brownian motion

1995 ◽  
pp. 237-247 ◽  
Author(s):  
J.-C. Gruet ◽  
Z. Shi
Keyword(s):  
Brownian Motion ◽  
Iterated Logarithm

The law of the iterated logarithm for Brownian sheets

1975 ◽  
Vol 12 (4) ◽  
pp. 840-844
Author(s):  
W. J. Park
Keyword(s):  
Banach Space ◽  
Brownian Motion ◽  
Iterated Logarithm ◽  
The Law

Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.

scholarly journals Approximation by Brownian motion for Gibbs measures and flows under a function

1984 ◽  
Vol 4 (4) ◽  
pp. 541-552 ◽  
Author(s):  
Manfred Denker ◽  
Walter Philipp
Keyword(s):  
Brownian Motion ◽  
Markov Chain ◽  
Gibbs Measures ◽  
Hölder Continuous ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
Image Position ◽  
Class Of Functions

AbstractLet denote a flow built under a Hölder-continuous function l over the base (Σ, μ) where Σ is a topological Markov chain and μ some (ψ-mining) Gibbs measure. For a certain class of functions f with finite 2 + δ-moments it is shown that there exists a Brownian motion B(t) with respect to μ and σ2 > 0 such that μ-a.e.for some 0 < λ < 5δ/588. One can also approximate in the same way by a Brownian motion B*(t) with respect to the probability . From this, the central limit theorem, the weak invariance principle, the law of the iterated logarithm and related probabilistic results follow immediately. In particular, the result of Ratner ([6]) is extended.

The increments of a bifractional Brownian motion

2009 ◽  
Vol 46 (4) ◽  
pp. 449-478 ◽  
Author(s):  
Charles El-Nouty
Keyword(s):  
Brownian Motion ◽  
Bifractional Brownian Motion ◽  
Iterated Logarithm

Let { BH;K ( t ), t ≧ 0} be a bifractional Brownian motion with indexes 0 < H < 1 and 0 < K ≦ 1 and define the statistic \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$V_T = \mathop {\sup }\limits_{0 \leqq s \leqq T - a_T } \beta _T \left| {B_{H,K} (s + a_T ) - B_{H,K} (s)} \right|$$ \end{document} where βT and αT are suitably chosen functions of T ≧ 0. We establish some laws of the iterated logarithm for VT .

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