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.

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.

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

Sample Path Properties of lp -Valued Ornstein-Uhlenbeck Processes

1990 ◽  
Vol 33 (3) ◽  
pp. 358-366 ◽  
Author(s):  
B. Schmuland
Keyword(s):  
Sample Path ◽  
Uhlenbeck Process ◽  
Sample Paths ◽  
Sample Path Properties ◽  
Ornstein Uhlenbeck Process ◽  
Zero Capacity ◽  
Vector Valued ◽  
Path Properties

AbstractWe give conditions under which a vector valued Ornstein Uhlenbeck process has continuous sample paths in lp for 1 ≦ p < ∞. We also show when the space lp is not entered at all, i.e., when it has zero capacity.

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

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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