scholarly journals Sample path properties of the local time of multifractional Brownian motion

Bernoulli ◽  
2007 ◽  
Vol 13 (3) ◽  
pp. 849-867 ◽  
Author(s):  
Brahim Boufoussi ◽  
Marco Dozzi ◽  
Raby Guerbaz
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Sample Path ◽  
Multifractional Brownian Motion ◽  
Sample Path Properties ◽  
Path Properties

scholarly journals Occupation time problem for multifractional Brownian motion

2019 ◽  
Vol 39 (1) ◽  
pp. 99-113
Author(s):  
Mohamed Ait Ouahra ◽  
Raby Guerbaz ◽  
Hanae Ouahhabi ◽  
Aissa Sghir
Keyword(s):  
Brownian Motion ◽  
Sample Path ◽  
Local Limit ◽  
Continuous Functions ◽  
Occupation Time ◽  
Local Times ◽  
Additive Functionals ◽  
Multifractional Brownian Motion ◽  
Sample Path Properties ◽  
Time Problem

In this paper, by using a Fourier analytic approach, we investigate sample path properties of the fractional derivatives of multifractional Brownian motion local times. We also show that those additive functionals satisfy a property of local asymptotic self-similarity. As a consequence, we derive some local limit theorems for the occupation time of multifractional Brownian motion in the space of continuous functions. 

scholarly journals Sample path properties of bifractional Brownian motion

Bernoulli ◽  
2007 ◽  
Vol 13 (4) ◽  
pp. 1023-1052 ◽  
Author(s):  
Ciprian A. Tudor ◽  
Yimin Xiao
Keyword(s):  
Brownian Motion ◽  
Sample Path ◽  
Bifractional Brownian Motion ◽  
Sample Path Properties ◽  
Path Properties

Scanning Brownian Processes

1997 ◽  
Vol 29 (02) ◽  
pp. 295-326 ◽  
Author(s):  
Robert J. Adler ◽  
Ron Pyke
Keyword(s):  
Brownian Motion ◽  
Random Field ◽  
Gaussian Random Field ◽  
Sample Path ◽  
Geometrical Properties ◽  
Basic Properties ◽  
Scanning Process ◽  
Sample Paths ◽  
Sample Path Properties ◽  
Path Properties

The ‘scanning process' Z(t), t ∈ ℝk of the title is a Gaussian random field obtained by associating with Z(t) the value of a set-indexed Brownian motion on the translate t + A 0 of some ‘scanning set' A 0. We study the basic properties of the random field Z relating, for example, its continuity and other sample path properties to the geometrical properties of A 0. We ask if the set A 0 determines the scanning process, and investigate when, and how, it is possible to recover the structure of A 0 from realisations of the sample paths of the random field Z.

Scanning Brownian Processes

1997 ◽  
Vol 29 (2) ◽  
pp. 295-326 ◽  
Author(s):  
Robert J. Adler ◽  
Ron Pyke
Keyword(s):  
Brownian Motion ◽  
Random Field ◽  
Gaussian Random Field ◽  
Sample Path ◽  
Geometrical Properties ◽  
Basic Properties ◽  
Scanning Process ◽  
Sample Paths ◽  
Sample Path Properties ◽  
Path Properties

The ‘scanning process' Z(t), t ∈ ℝk of the title is a Gaussian random field obtained by associating with Z(t) the value of a set-indexed Brownian motion on the translate t + A0 of some ‘scanning set' A0. We study the basic properties of the random field Z relating, for example, its continuity and other sample path properties to the geometrical properties of A0. We ask if the set A0 determines the scanning process, and investigate when, and how, it is possible to recover the structure of A0 from realisations of the sample paths of the random field Z.

Sample path behaviour of Χ2 surfaces at extrema

1988 ◽  
Vol 20 (4) ◽  
pp. 719-738 ◽  
Author(s):  
Michael Aronowich ◽  
Robert J. Adler
Keyword(s):  
Rough Surfaces ◽  
Sample Path ◽  
Gaussian Field ◽  
Random Surfaces ◽  
Sample Path Properties ◽  
Low Levels ◽  
Path Properties

We study the sample path properties of χ2 random surfaces, in particular in the neighbourhood of their extrema. We show that, as is the case for their Gaussian counterparts, χ2 surfaces at high levels follow the form of certain deterministic paraboloids, but that, unlike their Gaussian counterparts, at low levels their form is much more random. This has a number of interesting implications in the modelling of rough surfaces and the study of the ‘robustness' of Gaussian field models. The general approach of the paper is the study of extrema via the ‘Slepian model process', which, for χ2 fields, is tractable only at asymptotically high or low levels.

Sample path properties of the G/D/m queue

1993 ◽  
Vol 65 (2) ◽  
pp. 270-273
Author(s):  
Michael C. Fu ◽  
Jian-Qiang Hu
Keyword(s):  
Sample Path ◽  
Sample Path Properties ◽  
Path Properties
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