scholarly journals On pathwise projective invariance of Brownian motion, I

1988 ◽  
Vol 64 (2) ◽  
pp. 41-44 ◽  
Author(s):  
Shigeo Takenaka
Keyword(s):  
Brownian Motion ◽  
Projective Invariance

scholarly journals On projective invariance of Brownian motion

1968 ◽  
Vol 4 (3) ◽  
pp. 595-609 ◽  
Author(s):  
Takeyuki Hida ◽  
Izumi Kubo ◽  
Hisao Nomoto ◽  
Hisaaki Yoshizawa
Keyword(s):  
Brownian Motion ◽  
Projective Invariance

scholarly journals On Some Asymptotic Properties Concerning Brownian Motion

1952 ◽  
Vol 4 ◽  
pp. 97-101 ◽  
Author(s):  
Tunekiti Sirao ◽  
Tosio Nisida
Keyword(s):  
Brownian Motion ◽  
Random Sequence ◽  
Asymptotic Properties ◽  
Precise Result ◽  
Projective Invariance ◽  
Famous Book ◽  
Time Point

About the behavior of brownian motion at time point oo, there are many results by P. Lévy, A. Khintchine etc. P. Lévy cited a theorem by A. Kolmogoroff as the most precise result in his famous book “Processus stochastiques et mouvement brownian” without proof. In this paper we shall prove this theorem, using the similar result about the random sequence by W. Feller, and then, applying the theorem of projective invariance by P. Lévy, we shall find also the behavior of brownian motion at time point 0 from the above theorem.

On Projective Invariance of Brownian Motion

2001 ◽  
pp. 224-238
Author(s):  
Takeyuki HIDA ◽  
Izumi KUBO ◽  
Hisao NOMOTO ◽  
Hisaaki YOSHIZAWA
Keyword(s):  
Brownian Motion ◽  
Projective Invariance

scholarly journals On projective invariance of multi-parameter Brownian motion

1977 ◽  
Vol 67 ◽  
pp. 89-120 ◽  
Author(s):  
Shigeo Takenaka
Keyword(s):  
Brownian Motion ◽  
Random Field ◽  
White Noise ◽  
Radon Transform ◽  
Special Linear Group ◽  
Unitary Representations ◽  
View Point ◽  
Deep Insight ◽  
Structures And Properties ◽  
Projective Invariance

The multi-parameter Brownian motion introduced by P. Lévy is not only a basic random field but also gives us interesting fine probabilistic structures as well as important properties from the view point of analysis. We shall be interested in investigation of such structures and properties by expressing the Brownian motion in terms of the multiparameter white noise. The expression naturally requires basic tools from analysis, in particular the Radon transform. While there arises the special linear group SL(n + 1, R), to which the Radon transform is adapted, and the group plays an important role in observing probabilistic structures of the Brownian motion. To be more interested, we can give some deep insight to unitary representations of SL(n + 1, R) through our discussion.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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