Path properties of Cauchy’s principal values related to local time

2001 ◽  
Vol 38 (1-4) ◽  
pp. 149-169
Author(s):  
Éva Csáki ◽  
M. Csőrgő ◽  
A. Főldes ◽  
Z. Shi
Keyword(s):  
Random Walk ◽  
Strong Approximation ◽  
Sample Path ◽  
Local Times ◽  
Approximation Result ◽  
Cauchy Principal ◽  
Sample Path Properties ◽  
Small Increments ◽  
Path Properties ◽  
Exact Constants

Sample path properties of the Cauchy principal values of Brownian and random walk local times are studied. We establish LIL type results (without exact constants). Large and small increments are discussed. A strong approximation result between the above two processes is also proved.

scholarly journals Local times and sample path properties of the Rosenblatt process

2021 ◽  
Vol 131 ◽  
pp. 498-522
Author(s):  
George Kerchev ◽  
Ivan Nourdin ◽  
Eero Saksman ◽  
Lauri Viitasaari
Keyword(s):  
Sample Path ◽  
Local Times ◽  
Rosenblatt Process ◽  
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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