First Passage and First Exit Times for diffusion processes related to a general growth curve

Albano, Giuseppina; Barrera, Alberto; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

doi:10.1016/j.cnsns.2023.107494

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…The relevance of the FPT problem for diffusion processes modeling growth phenomena is well-known in the literature. In this framework, for brevity, we limit ourselves to recalling the recent results obtained in this area in Albano et al [37], where the FPT problem is faced for two stochastic forms of a general growth model in the presence of time-varying single or paired barriers.…”

Section: First-passage-time Problemmentioning

confidence: 99%

Stochastic Growth Models for the Spreading of Fake News

Di Crescenzo,

Paraggio,

Spina

2023

Mathematics

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The propagation of fake news in online social networks nowadays is becoming a critical issue. Consequently, many mathematical models have been proposed to mimic the related time evolution. In this work, we first consider a deterministic model that describes rumor propagation and can be viewed as an extended logistic model. In particular, we analyze the main features of the growth curve, such as the limit behavior, the inflection point, and the threshold-crossing-time, through fixed boundaries. Then, in order to study the stochastic counterparts of the model, we consider two different stochastic processes: a time non-homogeneous linear pure birth process and a lognormal diffusion process. The conditions under which the means of the processes are identical to the deterministic curve are discussed. The first-passage-time problem is also investigated both for the birth process and the lognormal diffusion process. Finally, in order to study the variability of the stochastic processes introduced so far, we perform a comparison between their variances.

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Section: First-passage-time Problemmentioning

confidence: 99%

Stochastic Growth Models for the Spreading of Fake News

Di Crescenzo,

Paraggio,

Spina

2023

Mathematics

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Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

Di Crescenzo,

Paraggio

2024

Math Methods in App Sciences

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We consider a two‐dimensional time‐inhomogeneous birth‐death process to model the time‐evolution of fake news in a population. The two components of the process represent, respectively: (i) the number of individuals (say spreaders) who know the rumor and intend to spread it and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function‐based approach to obtain the moments and the covariance of the two‐dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modeling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error.

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First Passage and First Exit Times for diffusion processes related to a general growth curve

Cited by 2 publications

References 28 publications

Stochastic Growth Models for the Spreading of Fake News

Stochastic Growth Models for the Spreading of Fake News

Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

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