Topic
Stochastic process
About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.
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TL;DR: In this article, the authors apply the extreme value theory of regenerative stochastic processes to the case of a set of n independent random variables with common distribution function F whose support consists of all sufficiently large positive integers.
Abstract: Let ξn be the maximum of a set of n independent random variables with common distribution function F whose support consists of all sufficiently large positive integers. Some of the classical asymptotic results of extreme value theory fail to apply to ξn for such F and this paper attempts to find weaker ones which give some description of the behaviour of ξn as n → ∞. These are then applied to the extreme value theory of certain regenerative stochastic processes.
159 citations
TL;DR: An intuitive approach to the stochastic network calculus is contributed, where the method uses moment generating functions, known from the theory of effective bandwidths, to characterize traffic arrivals and network service.
Abstract: The aim of the stochastic network calculus is to comprehend statistical multiplexing and scheduling of non-trivial traffic sources in a framework for end-to-end analysis of multi-node networks. To date, several models, some of them with subtle yet important differences, have been explored to achieve these objectives. Capitalizing on previous works, this paper contributes an intuitive approach to the stochastic network calculus, where we seek to obtain its fundamental results in the possibly easiest way. In detail, the method that is assembled in this work uses moment generating functions, known from the theory of effective bandwidths, to characterize traffic arrivals and network service. Thereof, affine envelope functions with an exponentially decaying overflow profile are derived to compute statistical end-to-end backlog and delay bounds for networks.
159 citations
TL;DR: In this article, the authors introduce a one-PRNG-per-kernel-call-perthread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call.
159 citations
TL;DR: In this paper, the envelope-constrained H ∞ filtering problem is investigated for a class of discrete time-varying stochastic systems over a finite horizon that involves fading measurements, randomly occurring nonlinearities and mixed noises.
158 citations