Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration

Giorno, Virginia; Nobile, Amelia Giuseppina

doi:10.3390/math8071123

Cited by 6 publications

(6 citation statements)

References 44 publications

(95 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For t ≥ t 0 and j ∈ N 0 , the probability generating function of the process N(t) is (cf. Giorno and Nobile [28]):…”

Section: Diffusion Approximation Of Birth-death Process With Immigrationmentioning

confidence: 99%

See 1 more Smart Citation

Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

Giorno

Nobile

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

The time-inhomogeneous Feller-type diffusion process, having infinitesimal drift α(t)x+β(t) and infinitesimal variance 2r(t)x, with a zero-flux condition in the zero-state, is considered. This process is obtained as a continuous approximation of a birth-death process with immigration. The transition probability density function and the related conditional moments, with their asymptotic behaviors, are determined. Special attention is paid to the cases in which the intensity functions α(t), β(t), r(t) exhibit some kind of periodicity due to seasonal immigration, regular environmental cycles or random fluctuations. Various numerical computations are performed to illustrate the role played by the periodic functions.

show abstract

“…For t ≥ t 0 and j ∈ N 0 , the probability generating function of the process N(t) is (cf. Giorno and Nobile [28]):…”

Section: Diffusion Approximation Of Birth-death Process With Immigrationmentioning

confidence: 99%

“…By virtue of ( 7), the transition probabilities p j,n (t|t 0 ) are obtained in Giorno and Nobile [28]. Furthermore, for t ≥ t 0 and j ∈ N 0 , the conditional mean and the conditional variance of…”

Section: Diffusion Approximation Of Birth-death Process With Immigrationmentioning

confidence: 99%

Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

Giorno

Nobile

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…where d n ) are the complete Bell polynomials defined in (31), with d k given in (32), from (C2) one obtains:…”

Section: Appendixmentioning

confidence: 99%

“…Indeed, in population dynamics the Feller-type diffusion process arises as a continuous approximation of a birth-death process with immigration (cf. Giorno and Nobile [32] and references therein). In these cases α(t), related to the growth intensity function, is positive (negative) when the birth intensity function is greater (less) than the death intensity function, whereas α(t) = 0 if the birth intensity function is equal to the death intensity function.…”

Section: Introductionmentioning

confidence: 97%

Time-Inhomogeneous Feller-type Diffusion Process with Absorbing Boundary Condition

Giorno

Nobile

2021

J Stat Phys

Self Cite

View full text Add to dashboard Cite

A time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift $$\alpha (t)x+\beta (t)$$ α ( t ) x + β ( t ) and linear infinitesimal variance 2r(t)x is considered. For this process, the transition density in the presence of an absorbing boundary in the zero-state and the first-passage time density through the zero-state are obtained. Special attention is dedicated to the proportional case, in which the immigration intensity function $$\beta (t)$$ β ( t ) and the noise intensity function r(t) are connected via the relation $$\beta (t)=\xi \,r(t)$$ β ( t ) = ξ r ( t ) , with $$0\le \xi <1$$ 0 ≤ ξ < 1 . Various numerical computations are performed to illustrate the effect of the parameters on the first-passage time density, by assuming that $$\alpha (t)$$ α ( t ) , $$\beta (t)$$ β ( t ) or both of these functions exhibit some kind of periodicity.

show abstract

“…In order to make them more realistic, it is possible to introduce a noise term, summarizing random fluctuations, in the differential equations (see Øksendal [28]) and to consider the resulting stochastic differential equations (as reported in Román-Román et al [29] and Di Crescenzo et al [7]). Other investigations have proposed introducing a random environment by considering special birth-death processes using an expected value which corresponds to the deterministic growth function (see Di Crescenzo and Spina [6], Di Crescenzo and Paraggio [3], Giorno and Nobile [30], Ricciardi [31]).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Growth Models for the Spreading of Fake News

Di Crescenzo,

Paraggio,

Spina

2023

Mathematics

View full text Add to dashboard Cite

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.

show abstract

Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration

Cited by 6 publications

References 44 publications

Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics

Time-Inhomogeneous Feller-type Diffusion Process with Absorbing Boundary Condition

Stochastic Growth Models for the Spreading of Fake News

Contact Info

Product

Resources

About