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Doubly stochastic Poisson processes
TLDR
In this article, the second order properties of stationary doubly stochastic Poisson sequences are estimated. But the second-order properties of random variables are not considered in this paper.Abstract:
Definitions and basic properties.- Some miscellaneous results.- Characterization and convergence of non-atomic random measures.- Limit theorems.- Estimation of random variables.- Linear estimation of random variables in stationary doubly stochastic Poisson sequences.- Estimation of second order properties of stationary doubly stochastic Poisson sequences.read more
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Foundations of modern probability
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Stochastic Geometry for Wireless Networks
TL;DR: This rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects.
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Autoregressive conditional duration: a new model for irregularly spaced transaction data
TL;DR: In this article, an autoregressive conditional duration (ACD) model is proposed for the analysis of data which arrive at irregular intervals, which treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates.
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Models for exceedances over high thresholds
Anthony C. Davison,Richard Smith +1 more
TL;DR: In this article, the authors discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds, and the natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated.
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On Cox Processes and Credit Risky Securities
TL;DR: It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default to reduce the technical issues of modeling credit risk.