Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Aquino, Gerardo; Palatella, Luigi; Grigolini, Paolo

doi:10.1590/s0103-97332005000300009

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…sequences then eq. ( 1) recovers the known expression for ordinary renewal process [18,49] i.e., f (u,…”

Section: A) B)supporting

confidence: 61%

Aging Renewal Point Processes and Exchangeability of Event Times

Vanni,

Lambert

2024

Preprint

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We investigate the impact of aging on exchangeable inter-arrival times in mixed renewal processes, exploring its implications for reliability and survival analysis. In this study, first, we revisit the definition of renewal point processes, where inter-event time intervals are considered as exchangeable non-negative random variables. Then, we define the concept of statistical aging as latency in the observational process of event counting. Latency affects event detection but preserves exchangeability. However, it may alter the statistical properties of inter-event time intervals. Our analytical and numerical assessments highlight the significance of aging in exchangeable lifetimes, offering insights into key metrics such as the failure survival function, renewal function, and hazard rate function. Through archetypal examples and empirical findings, we illustrate the implications of aging on renewal processes. In particular, employing a Bayesian perspective, we analyze high-frequency currency exchange rate data to assess the impact of aging on volatility risk evaluation. This study contributes novel insights to the literature of renewal theory and survival analysis, emphasizing the role of latency aging in stochastic point processes under exchangeability assumption.

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“…sequences then eq. ( 1) recovers the known expression for ordinary renewal process [18,49] i.e., f (u,…”

Section: A) B)supporting

confidence: 61%

Aging Renewal Point Processes and Exchangeability of Event Times

Vanni,

Lambert

2024

Preprint

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“…Let us note that, in the degenerate case of i.i.d. sequences, Equation (1) recovers the known expression for ordinary renewal process [23,55], i.e., f (u,…”

Section: Statistical Aging In Mixed Renewal Processesmentioning

confidence: 64%

Aging Renewal Point Processes and Exchangeability of Event Times

Vanni,

Lambert

2024

Mathematics

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In this paper, we investigate the impact of latency aging on exchangeable (invariant under permutation of indices) inter-arrival times arising from mixed renewal point processes (statistical mixtures of point processes with renewal inter-arrival times) and explore the implications for reliability and survival analysis. We prove that aging preserves the exchangeability of inter-arrival times. Our data analysis, which includes both surrogate data and a Bayesian approach to high-frequency currency exchange-rate data, shows how aging impacts key survival analysis metrics such as failure survival, renewal, and hazard rate functions.

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“…Considering the formal solution for the velocity of the charge, Equations ( 13 ) and (14), we need to evaluate the quantity

. For this purpose, we use the exact formula in the Laplace representation [ 24 , 25 ] (see Ref. [ 26 ] for detailed calculations)

where

is the Laplace transform of

and

(and consequently

is its Laplace transform) is the probability that no switch occurs for a generic interval of time t , i.e.,

…”

Section: Dichotomous Processesmentioning

confidence: 99%

Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field

Aquino

Chandía

Bologna

2021

Entropy

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In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous-Time Random Walk models.

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Absorption and emission in the non-poisson case: the theoretical challenge posed by renewal aging

Cited by 4 publications

References 27 publications

Aging Renewal Point Processes and Exchangeability of Event Times

Aging Renewal Point Processes and Exchangeability of Event Times

Aging Renewal Point Processes and Exchangeability of Event Times

Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field

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