2006
DOI: 10.1007/s10958-006-0041-x
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Logarithmic L 2-Small Ball Asymptotics with Respect to a Self-Similar Measure for Some Gaussian Processes

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Cited by 19 publications
(16 citation statements)
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“…We also note that some simple Gaussian processes with nonregular spectral asymptotics were considered in [Na2]. The problem of small ball behavior for fields-products when the eigenvalues of their factors are decreasing as in (1.6) is considerably more difficult than in the case of purely power decrease.…”
Section: Introductionmentioning
confidence: 99%
“…We also note that some simple Gaussian processes with nonregular spectral asymptotics were considered in [Na2]. The problem of small ball behavior for fields-products when the eigenvalues of their factors are decreasing as in (1.6) is considerably more difficult than in the case of purely power decrease.…”
Section: Introductionmentioning
confidence: 99%
“…Then N ⊗ (t) ∼ Cφ(1/t) t 1/p , t → +0, where φ(s) = (ϕ * ϕ)(s), and the constant C is defined in (8).…”
Section: Letmentioning
confidence: 99%
“…where p > 1, ψ is a SVF, and s is a continious periodic function. As an example of such an operator one might consider a Green integral operator with a singular arithmetically self-similar weight measure (see [6,7,8]). For the asymptotics (1) the following fact holds, which is similar to Lemma 3.1 from [4], so we will provide it without proof.…”
mentioning
confidence: 99%
“…In paper [11], this result is generalized to the case of a higher even order differential operator. It is also conjectured there that the function s is not constant for an arbitrary nonconstant weight with arithmetically self-similar primitive.…”
Section: Remarkmentioning
confidence: 99%