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 success of current attempts to distinguish between low-dimensional chaos and random behavior in a time series of observations is considered, and several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory.
329 citations
TL;DR: In this article, the results of [1] were used to establish equivalences between properties of the stochastic process and properties of sequences { Xn }, { n,u } and to evaluate, in terms of these sequences, some of the interesting probabilistic quantities associated with the process.
Abstract: In the applications one is given the matrix A and it is required to construct P(t) and to study the properties of the corresponding stochastic process. The existence, uniqueness, and the analytic properties of P(t) have been discussed in detail in [I]. The objective of this paper is to use the results of [1] to establish equivalences between properties of the stochastic process and properties of the sequences { Xn }, { n,u } and to evaluate, in terms of these sequences, some of the interesting probabilistic quantities associated with the process.
329 citations
TL;DR: This paper presents a method called PHI2 which is based on the outcrossing approach and allows to solve time-variant reliability problems using classical time-invariant reliability tools such as FORM/SORM methods.
328 citations
Book•
01 Jan 2003
TL;DR: The limit theorem for GI/GI/1 FIFO queues and random walks has been studied in this article, with a focus on the convergence of Stochastic Processes.
Abstract: 1 Point Processes- 2 GI/GI/1 FIFO Queues and Random Walks- 3 Limit Theorems for GI/GI/1 Queues- 4 Stochastic Networks and Reversibility- 5 The M/M/1 Queue- 6 The M/M/? Queue- 7 Queues with Poisson Arrivals- 8 Recurrence and Transience of Markov Chains- 9 Resealed Markov Processes and Fluid Limits- 10 Ergodic Theory: Basic Results- 11 Stationary Point Processes- 12 The G/G/1 FIFO Queue- A Martingales- A1 Discrete Time Parameter Martingales- A2 Continuous Time Martingales- A3 The Stochastic Integral for a Poisson Process- A4 Stochastic Differential Equations with Jumps- B Markovian Jump Processes- B2 Global Balance Equations- B3 The Associated Martingales- C Convergence in Distribution- C1 Total Variation Norm on Probability Distributions- C2 Convergence of Stochastic Processes- D An Introduction to Skorohod Problems- D1 Dimension 1- D2 Multi-Dimensional Skorohod Problems- References- Research Papers
328 citations