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Table Of Integrals Series And Products

Tables of integrals

(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

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An Introduction To The Theory Of Point Processes

Calderas are collapse structures related to the emptying of magmatic reservoirs, often associated with large eruptions from long-lived magmatic systems. Understanding how magma is transferred from a magma reservoir to the surface before eruptions is a major challenge. Here we exploit the historical, archaeological and geological record of Campi Flegrei caldera to estimate the surface deformation preceding the Monte Nuovo eruption and investigate the shallow magma transfer. Our data suggest a progressive magma accumulation from ~1251 to 1536 in a 4.6 ± 0.9 km deep source below the caldera centre, and its transfer, between 1536 and 1538, to a 3.8 ± 0.6 km deep magmatic source ~4 km NW of the caldera centre, below Monte Nuovo; this peripheral source fed the eruption through a shallower source, 0.4 ± 0.3 km deep. This is the first reconstruction of pre-eruptive magma transfer at Campi Flegrei and corroborates the existence of a stationary oblate source, below the caldera centre, that has been feeding lateral eruptions for the last ~5 ka. Our results suggest: 1) repeated emplacement of magma through intrusions below the caldera centre; 2) occasional lateral transfer of magma feeding non-central eruptions within the caldera. Comparison with historical unrest at calderas worldwide suggests that this behavior is common.

Magma transfer at Campi Flegrei caldera (Italy) before the 1538 AD eruption

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.

Analysis of random walks on a hexagonal lattice

We consider a discrete-time random walk on the nodes of a graphene-like graph, ie an unbounded hexagonal lattice We determine the probability generating functions, the transition probabilities and the relevant moments The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed Finally, we obtain some results on its asymptotic behavior making use of large deviation theory

Random walks on graphene: generating functions, state probabilities and asymptotic behavior

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subodinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in Di Crescenzo A., Macci C., Martinucci B. (2014).

Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the transition rates such that the transition probabilities satisfy a spatial symmetry relation. The latter leads to simple expressions for first-passage-time densities and avoiding transition probabilities. This approach is thus thoroughly extended to the case of bilateral birth-death processes, even in the presence of catastrophes, and to the case of a two-dimensional birth-death process with constant rates.

A review on symmetry properties of birth-death processes

We consider a telegraph process with elastic boundary at the origin studied recently in the literature (see eg Di Crescenzo et al (Methodol Comput Appl Probab 20:333–352 2018)) It is a particular random motion with finite velocity which starts at x ≥ 0, and its dynamics is determined by upward and downward switching rates λ and μ, with λ > μ, and an absorption probability (at the origin) α ∈ (0,1] Our aim is to study the asymptotic behavior of the absorption time at the origin with respect to two different scalings: $x\to \infty $
 in the first case; $\mu \to \infty $
 , with λ =β μ for some β > 1 and x > 0, in the second case We prove several large and moderate deviation results We also present numerical estimates of β based on an asymptotic Normality result for the case of the second scaling

Barbara Martinucci

Papers

Analysis of random walks on a hexagonal lattice

Random walks on graphene: generating functions, state probabilities and asymptotic behavior

Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

A review on symmetry properties of birth-death processes

Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin