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Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?
4 references·16 citing·45 second hop
Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion? (2002)Is Network Traffic Appriximated by Stable…Asymptotic results for multiplexing subexponential on-off processes (1999)Asymptotic results for multip…Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models (1998)Heavy Tails and Long Range De…Stopped Random Walks (1988)Stopped Random WalksExtreme Values, Regular Variation and Point Processes (1987)Extreme Values, Regular Varia…Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion (2019)Nonstationary self‐similar Ga…Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint (2018)Fractional Brownian motion wi…Realized Laplace transforms for pure-jump semimartingales (2012)Realized Laplace transforms f…Sensitivity Estimates from Characteristic Functions (2010)Sensitivity Estimates from Ch…Probabilistic Properties of Stochastic Volatility Models (2009)Probabilistic Properties of S…Activity signature functions for high-frequency data analysis (2009)Activity signature functions …Scaling Limits for Cumulative Input Processes (2007)Scaling Limits for Cumulative…Recent Advances in ARCH Modelling (2006)Recent Advances in ARCH Model…Modeling teletraffic arrivals by a Poisson cluster process (2006)Modeling teletraffic arrivals…A Limit Theorem for Financial Markets with Inert Investors (2006)A Limit Theorem for Financial…LASS: a tool for the local analysis of self-similarity (2005)LASS: a tool for the local an…Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed (2004)Slow, fast and arbitrary grow…SIMULATION METHODS FOR LINEAR FRACTIONAL STABLE MOTION AND FARIMA USING THE FAST FOURIER TRANSFORM (2004)SIMULATION METHODS FOR LINEAR…On a Class of Lévy Stochastic Networks (2004)On a Class of Lévy Stochastic…Generating schemes for long memory processes: regimes, aggregation and linearity (2004)Generating schemes for long m…Asymptotic independence and a network traffic model (2002)Asymptotic independence and a…Heavy tail modeling and teletraffic data: special invited paper (1997)Stochastic-process limits : an introduction to stochastic-process limits and their application to queues (2002)The Extremal Dependence Measure and Asymptotic Independence (2004)Hidden regular variation and the rank transform (2005)Precise large deviations of aggregate claims in a size-dependent renewal risk model (2012)Modelling of extremal events in insurance and finance (1994)Modelling Extremal Events (1997)Tails of random sums of a heavy-tailed number of light-tailed terms (2007)Asymptotics of randomly stopped sums in the presence of heavy tails (2010)Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues (2018)Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation (1982)Generalized autoregressive 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processes plus noise (2010)Nonparametric tests for pathwise properties of semimartingales (2011)Extreme Correlation of International Equity Markets (2001)Correlation and Dependence in Risk Management: Properties and Pitfalls (2002)The Asymptotic Efficiency of Simulation Estimators (1992)Large deviations of heavy-tailed random sums with applications in insurance and finance (1997)A stochastic mesh method for pricing high-dimensional American options (2004)
this work references cited by second hop

References

  • 1987Extreme Values, Regular Variation and Point Processes3,165 cited
  • 1988Stopped Random Walks384 cited
  • 1998Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models176 cited
  • 1999Asymptotic results for multiplexing subexponential on-off processes129 cited

Cited by

  • 2004SIMULATION METHODS FOR LINEAR FRACTIONAL STABLE MOTION AND FARIMA USING THE FAST FOURIER TRANSFORM130 cited
  • 2009Activity signature functions for high-frequency data analysis99 cited
  • 2006Modeling teletraffic arrivals by a Poisson cluster process80 cited
  • 2002Asymptotic independence and a network traffic model79 cited
  • 2004Generating schemes for long memory processes: regimes, aggregation and linearity78 cited
  • 2006Recent Advances in ARCH Modelling76 cited
  • 2005LASS: a tool for the local analysis of self-similarity72 cited
  • 2010Sensitivity Estimates from Characteristic Functions53 cited
  • 2006A Limit Theorem for Financial Markets with Inert Investors47 cited
  • 2009Probabilistic Properties of Stochastic Volatility Models46 cited
  • 2004Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed

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46 cited
  • 2012Realized Laplace transforms for pure-jump semimartingales31 cited
  • 2018Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint29 cited
  • 2007Scaling Limits for Cumulative Input Processes27 cited
  • 2019Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion27 cited
  • 2004On a Class of Lévy Stochastic Networks24 cited