Lévy's Brownian motion and total positivity

1983 ◽  
pp. 486-496
Author(s):  
Akio Noda
Keyword(s):  
Brownian Motion ◽  
Total Positivity

scholarly journals Lévy’s Brownian motion; Total positivity structure of M(t)-process and deterministic character

1984 ◽  
Vol 94 ◽  
pp. 137-164 ◽  
Author(s):  
Akio Noda
Keyword(s):  
Brownian Motion ◽  
Euclidean Space ◽  
Random Field ◽  
Hyperbolic Space ◽  
Parameter Space ◽  
Metric Space ◽  
Gaussian Random Field ◽  
Total Positivity ◽  
Time Parameter ◽  
Real Hyperbolic Space

Let X = {X(A); A ∈ Q} be a Lévy’s Brownian motion with the basic time parameter space Q, where Q is taken to be the n-dimensional metric space Qn,k of constant curvature (2 ≤ n ≤ ∞, — ∞ < k: < ∞), i.e., Q is one of(a) Euclidean space for k = 0, (b) sphere for k > 0 and(c) real hyperbolic space for K < 0.The increment X(A) — X(B) is, by definition, Gaussian in distribution and has mean 0 and variance d(A, B), the distance between A and B. The existence of such a Gaussian random field is well known ([3], [4], [16] and [23]).

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

A solution to Skorokhod's embedding for linear Brownian motion and its local time

2002 ◽  
Vol 39 (1-2) ◽  
pp. 97-127
Author(s):  
B. Roynette ◽  
P. Vallois
Keyword(s):  
Brownian Motion ◽  
Local Time

BROWNIAN MOTION

2006 ◽  
Vol b ◽  
Author(s):  
J. P.M Trusler
Keyword(s):  
Brownian Motion
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