Local asymptotic classes for the successive primitives of Brownian motion

DOI10.1214/aop/1023481108zbMath0903.60071OpenAlexW2020586873MaRDI QIDQ1381565

Aimé Lachal

Publication date: 18 March 1998

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1023481108

zbMATH Keywords

Brownian motionlaw of the iterated logarithmintegral testslocal asymptotic classes

Mathematics Subject Classification ID

Gaussian processes (60G15) Continuous-time Markov processes on general state spaces (60J25) Strong limit theorems (60F15) Brownian motion (60J65) Sample path properties (60G17)

Related Items (14)

A probabilistic study of the kinetic Fokker-Planck equation in cylindrical domains ⋮ A functional law of the iterated logarithm for weakly hypoelliptic diffusions at time zero ⋮ A necessary and sufficient condition of existence of global solutions for some nonlinear hyperbolic equations ⋮ Chung LIL for integrated \(\alpha\) stable process ⋮ Quadratic functionals and small ball probabilities for the \(m\)-fold integrated Brownian motion ⋮ The method of stochastic characteristics for linear second-order hypoelliptic equations ⋮ A functional LIL for \(m\)-fold integrated Brownian motion ⋮ A class of bridges of iterated integrals of Brownian motion related to various boundary value problems involving the one-dimensional polyharmonic operator ⋮ Path properties of the primitives of a Brownian motion ⋮ A functional LIL for integrated \(\alpha \) stable process ⋮ On convex least squares estimation when the truth is linear ⋮ Univariate log-concave density estimation with symmetry or modal constraints ⋮ Exact uniform modulus of continuity and Chung's LIL for the generalized fractional Brownian motion ⋮ Some \(\liminf\) results on increments of the primitives of Brownian motion

Cites Work

• On the general law of iterated logarithm with application to selfsimilar processes and to Gaussian processes in \(\mathbb{R}{}^ n\) and Hilbert space
• Asymptotic behavior of sample functions of Gaussian random fields
• A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement
• Regular points for the successive primitives of Brownian motion
• On the sample paths of the symmetric stable processes in spaces
• A winding problem for a resonator driven by a white noise
• [https://portal.mardi4nfdi.de/wiki/Publication:4085014 Sur la minoration asymptotique et le caract�re transitoire des trajectoires des fonctions al�atoires gaussiennes � valeurs dans R d]
• [https://portal.mardi4nfdi.de/wiki/Publication:4151459 Classes sup�rieures de processus gaussiens]
• A local asymptotic law for the transient stable process
• Radon-Nikodym Derivatives of Gaussian Measures
• Lower envelopes near zero and infinity for processes with stable components
• An Asymptotic Property of Gaussian Processes. I
• An Asymptotic 0-1 Behavior of Gaussian Processes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Local asymptotic classes for the successive primitives of Brownian motion