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 -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.
@article{AFST_2006_6_15_1_157_0, author = {Xiao, Yimin}, title = {Properties of local-nondeterminism of {Gaussian} and stable random fields and their applications}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {157--193}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 15}, number = {1}, year = {2006}, doi = {10.5802/afst.1117}, zbl = {1128.60041}, mrnumber = {2225751}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1117/} }
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 SP - 157 EP - 193 VL - 15 IS - 1 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1117/ DO - 10.5802/afst.1117 LA - en ID - AFST_2006_6_15_1_157_0 ER -
%0 Journal Article %A Xiao, Yimin %T Properties of local-nondeterminism of Gaussian and stable random fields and their applications %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2006 %P 157-193 %V 15 %N 1 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1117/ %R 10.5802/afst.1117 %G en %F AFST_2006_6_15_1_157_0
Xiao, Yimin. Properties of local-nondeterminism of Gaussian and stable random fields and their applications. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 1, pp. 157-193. doi : 10.5802/afst.1117. http://archive.numdam.org/articles/10.5802/afst.1117/
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