An asymptotic property of Gaussian processes. I

Watanabe, Hisao

doi:10.1090/s0002-9947-1970-0256478-5

Cited by 32 publications

(25 citation statements)

References 11 publications

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“…This result includes Theorem A and Theorem 5 in [15] as special cases, and implies the first two inequalities in (1.1). It also extends previous works of the author on the increments of FWP [7,8].…”

Section: Ix(t+a~)-x(t)] A(a)supporting

confidence: 59%

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Upper classes for the increments of fractional Wiener processes

Ortega

1989

Probab. Th. Rel. Fields

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Section: Ix(t+a~)-x(t)] A(a)supporting

confidence: 59%

“…A similar proof shows that q~ ~UUC(Y*)., if /3=1 then Theorem 5 in[15] implies the result. A similar proof shows that q~ ~UUC(Y*)., if /3=1 then Theorem 5 in[15] implies the result.…”

mentioning

confidence: 65%

Upper classes for the increments of fractional Wiener processes

Ortega

1989

Probab. Th. Rel. Fields

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“…The purpose of this paper is to investigate the asymptotic 0-1 behavior of the processes Q B H . Our first contribution is an analog of the classical finding of Watanabe (1970), where an asymptotic 0-1 type of behavior for centered stationary Gaussian processes was analyzed.…”

Section: Q B H (T) = Sup −∞mentioning

confidence: 99%

An Erdös–Révész type law of the iterated logarithm for reflected fractional Brownian motion

Dȩbicki

Kosinski

2017

Extremes

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“…In further analysis we tacitly assume that the variance function σ 2 of X satisfies both AI and AII. Our first contribution is the following criterion; see, e.g., Watanabe (1970); Qualls and Watanabe (1971) for similar results in the classical setting of non-reflected stationary Gaussian process.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Sample path properties of reflected Gaussian processes

Kosinski¹,

Liu²

2018

ALEA

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We consider a stationary queueing process Q X fed by a centered Gaussian process X with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function f , P(Q X (t) > f (t) i.o.) equals 0 or 1 is provided. Furthermore, an Erdös-Révész type law of the iterated logarithm is proven for the last passage time ξ(t) = sup{s : 0 ≤ s ≤ t, Q X (s) ≥ f (s)}. Both of these findings extend previously known results that were only available for the case when X is a fractional Brownian motion.

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An asymptotic property of Gaussian processes. I

Cited by 32 publications

References 11 publications

Upper classes for the increments of fractional Wiener processes

Upper classes for the increments of fractional Wiener processes

An Erdös–Révész type law of the iterated logarithm for reflected fractional Brownian motion

Sample path properties of reflected Gaussian processes

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