2020
DOI: 10.3390/math8040588
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Abstract: In this paper, we study a new family of Gompertz processes, defined by the power of the homogeneous Gompertz diffusion process, which we term the powers of the stochastic Gompertz diffusion process. First, we show that this homogenous Gompertz diffusion process is stable, by power transformation, and determine the probabilistic characteristics of the process, i.e., its analytic expression, the transition probability density function and the trend functions. We then study the statistical inference in this proce… Show more

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Cited by 6 publications
(7 citation statements)
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References 34 publications
(40 reference statements)
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“…Theoretical studies on the growth of the tree-size components proved that the tree-size-component frequency distribution is characterized by many small trees and few larger trees [35]. For the bivariate Gompertz-type diffusion process, it is possible to derive the stationary univariate marginal and conditional distributions if parameters βd and βh are positive [36]. As time, t, goes to infinity for the Gompertz-type diffusion, the diameter and height marginal distributions (see Table 1) and conditional distributions (see Table 3) converge to a lognormal stationary distribution with the means and variances listed in Table 10 ( ∈ { , ℎ}).…”
Section: Comparison Of Diameter Height Height-diameter and Diametementioning
confidence: 99%
“…Theoretical studies on the growth of the tree-size components proved that the tree-size-component frequency distribution is characterized by many small trees and few larger trees [35]. For the bivariate Gompertz-type diffusion process, it is possible to derive the stationary univariate marginal and conditional distributions if parameters βd and βh are positive [36]. As time, t, goes to infinity for the Gompertz-type diffusion, the diameter and height marginal distributions (see Table 1) and conditional distributions (see Table 3) converge to a lognormal stationary distribution with the means and variances listed in Table 10 ( ∈ { , ℎ}).…”
Section: Comparison Of Diameter Height Height-diameter and Diametementioning
confidence: 99%
“…In addition to traditional applications, stochastic diffusion processes (SDPs) have attracted considerable attention as analytical tools in areas such as cell growth, population growth and environmental studies. In this respect, see for example: Lognormal [1]; Gompertz [2]; Logistic [3]; Hyperbolic [4]; Rayleigh [5]; Pearson [6]; Weibull [7] and Brennan-Schwartz [8].…”
Section: Introductionmentioning
confidence: 99%
“…Moreover, various efforts are direct to computational approaches (Di Nardo et al [18], Taillefumier and Magnasco [19], D'Onofrio and Pirozzi [20]) that also involve methods of statistical inferences (Albano et al [21], Albano and Giorno [22], Ramos-Ábalos et al [23]). Specifically, in Di Nardo et al [18] and Taillefumier and Magnasco [19] methods to construct first-passage-time probability density functions for Gauss-Markov processes through timedependent boundaries are proposed.…”
Section: Introductionmentioning
confidence: 99%
“…In D'Onofrio and Pirozzi [20], the problem of escape times from a region confined by two time-dependent boundaries is considered for a class of Gauss-Markov processes. Moreover, numerical procedures to infer the models based on time-inhomogeneous diffusion processes are proposed in Albano et al [21], Albano and Giorno [22], and Ramos-Ábalos et al [23].…”
Section: Introductionmentioning
confidence: 99%