TY - JOUR

T1 - Tail approximation in models that involve long range dependence

T2 - The distribution of overflows

AU - Yakir, Benjamin

PY - 2013/7

Y1 - 2013/7

N2 - Long range dependence in stationary processes of increments corresponds to the situations where the variance of cumulative sums is dominated by the accumulation of the covariances between increments. The Hurst parameter, the exponent of the standard deviation of the sum as a function of the number of increments involved, is a characteristic of long range dependence. Models of long range dependence, models that involve an Hurst parameter 0:5 < H < 1, are frequently used to model the incoming workload in computer networks and communication. Consider a Gaussian arrival process with long range dependence, a buffer, and a departure process bounded by the bandwidth. This paper present an analytical approximations of the probability of a buffer overflow within a given time interval. The analysis uses and demonstrates a measure-transformation technique.

AB - Long range dependence in stationary processes of increments corresponds to the situations where the variance of cumulative sums is dominated by the accumulation of the covariances between increments. The Hurst parameter, the exponent of the standard deviation of the sum as a function of the number of increments involved, is a characteristic of long range dependence. Models of long range dependence, models that involve an Hurst parameter 0:5 < H < 1, are frequently used to model the incoming workload in computer networks and communication. Consider a Gaussian arrival process with long range dependence, a buffer, and a departure process bounded by the bandwidth. This paper present an analytical approximations of the probability of a buffer overflow within a given time interval. The analysis uses and demonstrates a measure-transformation technique.

KW - Cusum

KW - Likelihood-ratio identity

KW - Long-range dependence

KW - Maxima of a random field

KW - Overshoot correction

UR - http://www.scopus.com/inward/record.url?scp=84884166380&partnerID=8YFLogxK

U2 - 10.5705/ss.2012.100s

DO - 10.5705/ss.2012.100s

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AN - SCOPUS:84884166380

SN - 1017-0405

VL - 23

SP - 1657

EP - 1672

JO - Statistica Sinica

JF - Statistica Sinica

IS - 4

ER -