scholarly journals Occupation times of alternating renewal processes with Lévy applications

2018 ◽  
Vol 55 (4) ◽  
pp. 1287-1308 ◽  
Author(s):  
Nicos Starreveld ◽  
Réne Bekker ◽  
Michel Mandjes
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variable ◽  
Levy Processes ◽  
Normal Random Variable ◽  
Occupation Time ◽  
Renewal Processes ◽  
Tail Asymptotics ◽  
Occupation Times

AbstractIn this paper we present a set of results relating to the occupation time α(t) of a processX(·). The first set of results concerns exact characterizations of α(t), e.g. in terms of its transform up to an exponentially distributed epoch. In addition, we establish a central limit theorem (entailing that a centered and normalized version of α(t)∕tconverges to a zero-mean normal random variable ast→∞) and the tail asymptotics of ℙ(α(t)∕t≥q). We apply our findings to spectrally positive Lévy processes reflected at the infimum and establish various new occupation time results for the corresponding model.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

scholarly journals The central limit theorem for the sums of the discrete renewal processes

1969 ◽  
Vol 9 (3) ◽  
pp. 497-514
Author(s):  
B. Kaminskienė
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Renewal Processes ◽  
The Central Limit Theorem

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Каминскене. Центральная предельная теорема для сумм дискретных процессов восстановления B. Kaminskienė. Centrinė ribinė teorema diskretinių atstatymo procesų sumoms

scholarly journals The central limit theorem for sums of the renewal processes

1968 ◽  
Vol 8 (4) ◽  
pp. 617-631
Author(s):  
A. Aleškevičienė
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Renewal Processes ◽  
The Central Limit Theorem

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: А. Алешкявичене. Центральная предельная теорема для сумм процессов восстановления A. Aleškevičienė. Centrinė ribinė teorema atstatymo procesų sumoms

A Note On The Calculation And Application Of The Third Absolute Central Moment Of Chi-square Distribution

1992 ◽  
pp. 83-86
Author(s):  
Abu Hassan Shaari Mohd Nor ◽  
Fauziah Maarof
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variable ◽  
Central Moment ◽  
Chi Square ◽  
Exact Bound ◽  
The Third ◽  
The Central Limit Theorem ◽  
Numerical Integrations

Kertas ini mengemukakan satu cara mencari momen memusat mutlak ketiga bagi pembolehubah rawak khi-kuasadua. Aturcara SAS (1988) iaitu PROBCHI digunakan bagi menyelesaikan pengamiran berangka. Kegunaannya dalam membina batas yang tepat ke atas ralat penghampiran dalam Teorem Had Memusat diberikan. This paper presents a way of calculating the third absolute central moment of a chi-square random variable. The SAS (1988) function PROBCHI is used to evaluate the numerical integrations. An application of this result in the construction of an exact bound on the error of approximation in the Central Limit Theorem is presented.

On the asymptotic distribution of multivariate renewal processes

1984 ◽  
Vol 21 (3) ◽  
pp. 639-645 ◽  
Author(s):  
Ştefan P. Niculescu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Asymptotic Distribution ◽  
Central Limit ◽  
Renewal Theory ◽  
Renewal Processes ◽  
Limit Distributions ◽  
Multidimensional Central Limit Theorem

Using a result of Bikjalis (1971) concerning the rate of convergence in the multidimensional central limit theorem we obtain informations about some limit distributions in multivariate renewal theory.

Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs

1998 ◽  
Vol 01 (02) ◽  
pp. 221-246 ◽  
Author(s):  
Akihito Hora
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variable ◽  
Spectral Structure ◽  
Regular Graphs ◽  
Large Graphs ◽  
The Central Limit Theorem ◽  
Distance Regular Graphs

Regarding the adjacency matrix of a graph as a random variable in the framework of algebraic or noncommutative probability, we discuss a central limit theorem in which the size of a graph grows in several patterns. Various limit distributions are observed for some Cayley graphs and some distance-regular graphs. To obtain the central limit theorem of this type, we make combinatorial analysis of mixed moments of noncommutative random variables on one hand, and asymptotic analysis of spectral structure of the graph on the other hand.

scholarly journals On mixing and the local central limit theorem for hyperbolic flows

2018 ◽  
Vol 40 (1) ◽  
pp. 142-174 ◽  
Author(s):  
DMITRY DOLGOPYAT ◽  
PÉTER NÁNDORI
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Finite Horizon ◽  
Suspension Flow ◽  
Renewal Processes ◽  
Axiom A ◽  
Hyperbolic Flows ◽  
Local Central Limit Theorem ◽  
Lorenz Attractors

We formulate abstract conditions under which a suspension flow satisfies the local central limit theorem. We check the validity of these conditions for several systems including reward renewal processes, Axiom A flows, as well as the systems admitting Young’s tower, such as Sinai’s billiard with finite horizon, suspensions over Pomeau–Manneville maps, and geometric Lorenz attractors.

scholarly journals A Central Limit Theorem for a Discrete-Time SIS Model with Individual Variation

2012 ◽  
Vol 49 (2) ◽  
pp. 521-530 ◽  
Author(s):  
R. McVinish ◽  
P. K. Pollett
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Discrete Time ◽  
Random Variable ◽  
Metapopulation Model ◽  
Sis Model ◽  
Susceptibility To Infection ◽  
Rate Of Recovery ◽  
Nonzero Mean

A discrete-time SIS model is presented that allows individuals in the population to vary in terms of their susceptibility to infection and their rate of recovery. This model is a generalisation of the metapopulation model presented in McVinish and Pollett (2010). The main result of the paper is a central limit theorem showing that fluctuations in the proportion of infected individuals around the limiting proportion converges to a Gaussian random variable when appropriately rescaled. In contrast to the case where there is no variation amongst individuals, the limiting Gaussian distribution has a nonzero mean.

On the asymptotic distribution of multivariate renewal processes

1984 ◽  
Vol 21 (03) ◽  
pp. 639-645 ◽  
Author(s):  
Ştefan P. Niculescu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Asymptotic Distribution ◽  
Central Limit ◽  
Renewal Theory ◽  
Renewal Processes ◽  
Limit Distributions ◽  
Multidimensional Central Limit Theorem

Using a result of Bikjalis (1971) concerning the rate of convergence in the multidimensional central limit theorem we obtain informations about some limit distributions in multivariate renewal theory.

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