Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces
نویسندگان
چکیده
This paper is concerned with sample path properties of real-valued isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property strong local nondeterminism an field and then exploit this result to exact uniform modulus continuity for its paths.
منابع مشابه
Strong Local Nondeterminism and Sample Path Properties of Gaussian Random Fields
Sufficient conditions for a real-valued Gaussian random field X = {X(t), t ∈ RN} with stationary increments to be strongly locally nondeterministic are proven. As applications, small ball probability estimates, Hausdorff measure of the sample paths, sharp Hölder conditions and tail probability estimates for the local times of Gaussian random fields are established. Running head: Strong Local No...
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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...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2023
ISSN: ['1572-9230', '0894-9840']
DOI: https://doi.org/10.1007/s10959-022-01231-8