A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation

Nafidi, Ahmed; Azri, Abdenbi El

doi:10.1016/j.matcom.2020.10.022

Cited by 12 publications

(8 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Examples of the observable variables are the body weight and body size, while the latent variables include the history-dependent maximum body weight [19,35] and dynamically changing energetic variables [36][37]. Temporally inhomogeneous models can also be seen as open-ended growth models where time-dependent parameters add a flexibility in modeling the growth curves [38][39][40][41]. Hence, we need to find a mathematical framework that depends only on the observable variables.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

Yoshioka

Tanaka

Aranishi

et al. 2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In inland fisheries, transporting fishery resource individuals from a habitat to spatially apart habitat(s) has recently been considered for fisheries stock management in the natural environment. However, its mathematical optimization, especially finding when and how much of the population should be transported, is still a fundamental unresolved issue. We propose a new impulse control framework to tackle this issue based on a simple but new stochastic growth model of individual fishes. The novel growth model governing individuals' body weights uses a Wright-Fisher model as a latent driver to reproduce plausible growth dynamics. The optimization problem is formulated as an impulse control problem of a cost-benefit functional constrained by a degenerate parabolic Fokker-Planck equation of the stochastic growth dynamics.Because the growth dynamics have an observable variable and an unobservable variable (a variable difficult or impossible to observe), we consider both full-information and partial-information cases. The latter is more involved but more realistic because of not explicitly using the unobservable variable in designing the controls. In both cases, resolving an optimization problem reduces to solving the associated Fokker-Planck and its adjoint equations, the latter being non-trivial. We present a derivation procedure of the adjoint equation and its internal boundary conditions in time to efficiently derive the optimal transporting strategy.We finally provide a demonstrative computational example of a transporting problem of Ayu sweetfish (Plecoglossus altivelis altivelis) based on the latest real data set.

show abstract

Section: Mathematical Backgroundmentioning

confidence: 99%

“…Now, we get the necessary optimality condition from (41). As in Theorem 3.2 of De los Reyes [24], we have the necessary optimality condition…”

mentioning

confidence: 98%

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

Yoshioka

Tanaka

Aranishi

et al. 2021

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…The question of estimating parameters of the drift coefficient has received considerable attention of researchers in recent years, both when the process is observed continuously and when it is discrete. Various authors address this question, and many papers have been published on this subject, focusing on the simulated annealing (SA) algorithm for the problem of maximum likelihood (ML) estimation, such as Nafidi and El Azri [6], Nafidi et al [7] and Román-Román et al [10].…”

Section: Introductionmentioning

confidence: 99%

A γ-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation

Abdenbi

Nafidi

2022

Moroccan Journal of Pure and Applied Analysis

View full text Add to dashboard Cite

In this paper, we introduce a new family of stochastic Lundqvist-Korf diffusion process, defined from a g-power of the Lundqvist-Korf diffusion process. First, we determine the probabilistic characteristics of the process, such as its analytic expression, the transition probability density function from the corresponding It ˆo stochastic differential equation and obtain the conditional and non-conditional mean functions. We then study the statistical inference in this process. The parameters of this process are estimated by using the maximum likelihood estimation method with discrete sampling, thus we obtain a nonlinear equation, which is achieved via the simulated annealing algorithm. Finally, the results of the paper are applied to simulated data.

show abstract

“…It can be applied to forest mensuration, such as the relation between height and age for three black spruce stands. Nafidi and El Azri [24] proposed a new non-homogeneous SDP in which the trend function is proportional to the growth curve of the Lundqvist-Korf. Crescenzo et al [5] and [6] introduced a new deterministic growth model which captures certain features of both the Gompertz and Korf laws.…”

Section: Introductionmentioning

confidence: 99%

“…Duflo [7] used for optimization in continuous spaces the method models the physical process of heating a material and then slowly lowering the temperature to decrease defects, thus minimizing the system energy. Recently, many works have used the SA algorithm for estimating the parameters in the stochastic diffusion process (see, for instance, Nafidi and El Azri [24] and Nafidi et al [23]).…”

Section: Introductionmentioning

confidence: 99%

The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

Nafidi

Azri

Sánchez

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The main goal of this paper is to study the possibility of using a stochastic non-homogeneous (without exogenous factors) diffusion process to model the evolution of CO2 emissions in Morocco and concretely using a new process, in which the trend function is proportional to the modified Lundqvist-Korf growth curve. First, the main characteristics of the process are studied, then we establish a computational statistical methodology based on the maximum likelihood estimation method and the trend functions. When we are estimating the parameters of the process, a non-linear equation is obtained and the simulated annealing method is proposed to solve it after bounding the parametric space by a stagewise procedure. Also, to validate this methodology, we include the results obtained from several examples of simulation. Finally, the process and the methodology established are applied to real data corresponding to the evolution of CO2 emissions in Morocco.

show abstract

A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation

Cited by 12 publications

References 25 publications

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

Impulsive fishery resource transporting strategies based on an open‐ended stochastic growth model having a latent variable

A γ-power stochastic Lundqvist-Korf diffusion process: Computational aspects and simulation

The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

Contact Info

Product

Resources

About