
Records for Some Stationary Dependence Sequences
For a zeromean, unitvariance secondorder stationary univariate Gaussi...
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Extremal clustering in nonstationary random sequences
It is well known that the distribution of extreme values of strictly sta...
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Breaking Bivariate Records
We establish a fundamental property of bivariate Pareto records for inde...
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Joint Probability Distribution of Prediction Errors of ARIMA
Producing probabilistic guarantee for several steps of a predicted signa...
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Exact and asymptotic properties of δrecords in the linear drift model
The study of records in the Linear Drift Model (LDM) has attracted much ...
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Generating Pareto records
We present, (partially) analyze, and apply an efficient algorithm for th...
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The Moran Genealogy Process
We give a novel representation of the Moran Genealogy Process, a continu...
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Records for Some Stationary Dependent Sequences
For a zeromean, unitvariance secondorder stationary univariate Gaussian process we derive the probability that a record at the time n, say X_n, takes place and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between the first and second record, and the third and second record and we compute the expected number of records. We also consider two consecutive and nonconsecutive records, one at time j and one at time n and we derive the probability that the joint records (X_j,X_n) occur as well as their distribution function. The probability that the records X_n and (X_j,X_n) take place and the arrival time of the nth record, are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a secondorder stationary process with Gaussian copulas. We extend some of these results to the case of a multivariate Gaussian process. Finally, for a strictly stationary process satisfying some mild conditions on the tail behavior of the common marginal distribution function F and the longrange dependence of the extremes of the process, we derive the asymptotic probability that the record X_n occurs and derive its distribution function.
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