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, p. 157-193

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.

@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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 15},
     number = {1},
     year = {2006},
     pages = {157-193},
     doi = {10.5802/afst.1117},
     mrnumber = {2225751},
     zbl = {1128.60041},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AFST_2006_6_15_1_157_0/

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