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Table Of Integrals Series And Products

Tables of integrals

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

Comparing first-passage times for semi-Markov skip-free processes☆

A spatial symmetry property of a two-dimensional birth–death process X(t) with constant rates is exploited in order to obtain closed-form expressions for first-passage-time densities through straight-lines x 2 = x 1 + r and for the related taboo transition probabilities. An analogous study is performed on a birth–death process with state-dependent rates that is similar to X(t) in the sense that the ratio of their transition functions is time independent. Examples of applications to double-ended queues and stochastic neuronal modeling are also provided.

A First-Passage-Time Problem for Symmetric and Similar Two-Dimensional Birth–Death Processes

In reliability theory and survival analysis, the residual entropy is known as a measure suitable to describe the dynamic information content in stochastic systems conditional on survival. Aiming to analyze the variability of such information content, in this paper we introduce the variance of the residual lifetimes, "residual varentropy" in short. After a theoretical investigation of some properties of the residual varentropy, we illustrate certain applications related to the proportional hazards model and the first-passage times of an Ornstein-Uhlenbeck jump-diffusion process.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/63586856E88C9703FA90028F16B3CD4A/S0269964820000133a.pdf/div-class-title-analysis-and-applications-of-the-residual-varentropy-of-random-lifetimes-div.pdf

Analysis and applications of the residual varentropy of random lifetimes

Analysis of reliability systems via Gini-type index

Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.

Antonio Di Crescenzo

Papers

Comparing first-passage times for semi-Markov skip-free processes☆

A First-Passage-Time Problem for Symmetric and Similar Two-Dimensional Birth–Death Processes

Analysis and applications of the residual varentropy of random lifetimes

Analysis of reliability systems via Gini-type index

A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation