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Extreme Values, Regular Variation, and Point Processes

- S. Resnick
- Mathematics
- 21 July 1987

Contents: Preface * Preliminaries * Domains of Attraction and Norming Constants * Quality of Convergence * Point Processes * Records and Extremal Processes * Multivariate Extremes * References *… Expand

Heavy-Tail Phenomena: Probabilistic and Statistical Modeling

- S. Resnick
- Mathematics
- 1 December 2006

Crash Courses.- Crash Course I: Regular Variation.- Crash Course II: Weak Convergence Implications for Heavy-Tail Analysis.- Statistics.- Dipping a Toe in the Statistical Water.- Probability.- The… Expand

A Probability Path

- S. Resnick
- Mathematics
- 1999

1 Sets and Events.- 2 Probability Spaces.- 3 Random Variables, Elements and Measurable Maps.- 4 Independence.- 5 Integration and Expectation.- 6 Convergence Concepts.- 7 Laws of Large Numbers and… Expand

Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities

- R. Davis, S. Resnick
- Mathematics
- 1 February 1985

Let 1Zk, -00 < k < ooj be iid where the Zk's have regularly varying tail probabilities. Under mild conditions on a real sequence fcj, j 2 0) the stationary process fX,: = ,=t c1Z,,.., n 2 1) exists.… Expand

Extreme values of independent stochastic processes

- B. M. Brown, S. Resnick
- MathematicsJournal of Applied Probability
- 1 December 1977

The maxima of independent Weiner processes spatially normalized with time scales compressed is considered and it is shown that a weak limit process exists. This limit process is stationary, and its… Expand

Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages

- R. Davis, S. Resnick
- Mathematics
- 1 June 1986

Abstract : Document describes a moving average process which have regularly varying tail probabilities with index alpha 0. The limit distribution of the sample covariance function is derived in the… Expand

Point processes, regular variation and weak convergence

- S. Resnick
- MathematicsAdvances in Applied Probability
- 1 March 1986

A method is reviewed for proving weak convergence in a function-space setting when regular variation is a sufficient condition. Point processes and weak convergence techniques involving continuity… Expand

Adventures in stochastic processes

- S. Resnick
- Mathematics
- 1992

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many… Expand

Is network traffic approximated by stable Levy motion or fractional Brownian motion

- T. Mikosch, S. Resnick, H. Rootzén, A. Stegeman
- Mathematics
- 1 February 2002

Cumulative broadband network traffic is often thought to be well
modeled by fractional Brownian motion (FBM). However, some traffic
measurements do not show an agreement with the Gaussian marginal… Expand

Limit theory for multivariate sample extremes

- L. Haan, S. Resnick
- Mathematics
- 1 December 1977

SummaryLet
$$\{ (X_n^{(1)} ),...,X_n^{(k)} ,{\text{ }}n\} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } 1\} $$
be k-dimensional iid random vectors. Necessary and… Expand

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