Properties of local-nondeterminism of Gaussian and stable random fields and their applications

Yimin Xiao[1]

  • [1] Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, MI 48824.

Annales de la faculté des sciences de Toulouse Mathématiques (2006)

  • Volume: 15, Issue: 1, page 157-193
  • ISSN: 0240-2963

Abstract

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In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of ( N , d ) -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the Brownian sheet, fractional Brownian sheets and so on.

How to cite

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Xiao, Yimin. "Properties of local-nondeterminism of Gaussian and stable random fields and their applications." Annales de la faculté des sciences de Toulouse Mathématiques 15.1 (2006): 157-193. <http://eudml.org/doc/10031>.

@article{Xiao2006,
abstract = {In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of $(N, d)$-Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the Brownian sheet, fractional Brownian sheets and so on.},
affiliation = {Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, MI 48824.},
author = {Xiao, Yimin},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Gaussian; stable; random fields; nondeterminism; sample path; law of the iterated logarithm; local time},
language = {eng},
number = {1},
pages = {157-193},
publisher = {Université Paul Sabatier, Toulouse},
title = {Properties of local-nondeterminism of Gaussian and stable random fields and their applications},
url = {http://eudml.org/doc/10031},
volume = {15},
year = {2006},
}

TY - JOUR
AU - Xiao, Yimin
TI - Properties of local-nondeterminism of Gaussian and stable random fields and their applications
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2006
PB - Université Paul Sabatier, Toulouse
VL - 15
IS - 1
SP - 157
EP - 193
AB - In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of $(N, d)$-Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the Brownian sheet, fractional Brownian sheets and so on.
LA - eng
KW - Gaussian; stable; random fields; nondeterminism; sample path; law of the iterated logarithm; local time
UR - http://eudml.org/doc/10031
ER -

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