Properties of local-nondeterminism of Gaussian and stable random fields and their applications
نویسندگان
چکیده
— 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. RÉSUMÉ. — 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.
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Strong Local Nondeterminism and Sample Path Properties of Gaussian Random Fields
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