(r, p)-Capacity on the Wiener space and properties of Brownian motion

1984 ◽  
Vol 68 (2) ◽  
pp. 149-162 ◽  
Author(s):  
Masayoshi Takeda
Keyword(s):  
Brownian Motion ◽  
Wiener Space

On homogeneous chaos

1991 ◽  
Vol 110 (2) ◽  
pp. 353-363 ◽  
Author(s):  
Nigel Cutland ◽  
Siu-Ah Ng
Keyword(s):  
Brownian Motion ◽  
Wiener Space ◽  
Chaos Decomposition ◽  
Image Position

AbstractThis paper discusses the Wiener–Itô chaos decomposition of an L2 function φ over Wiener space, and is concerned in particular with the identification of the integrands ƒn in the chaos decompositionFirst these are identified as Radon–Nikodým derivatives. Two elementary non-standard proofs of the Wiener–Itô chaos decomposition are given, based on Anderson's construction of Brownian motion and Itô integration.

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.

Model demonstration of brownian motion

1971 ◽  
Vol 105 (12) ◽  
pp. 736-736
Author(s):  
V.I. Arabadzhi
Keyword(s):  
Brownian Motion
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