A boundary preserving numerical scheme for the Wright–Fisher model

Stamatiou, Ioannis S.

doi:10.1016/j.cam.2017.07.011

Cited by 15 publications

(10 citation statements)

References 14 publications

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“…We can use numerical schemes to simulate bounded numerical solutions inheriting this property [52], further supporting usefulness of the proposed model in applications.…”

Section: ( ) ( )supporting

confidence: 52%

“…This performance measure is a sum of the relative errors of the first-order to the third-order statistics and a minimizing model should be able to capture the distributional shape of the observed histogram both qualitatively and quantitatively. The system (4) is numerically simulated using a Monte-Carlo method based on the bounded scheme [52] for the SDE of Z and the classical Euler-Maruyama scheme for the SDE of W . Each sample path generated by the Monte-Carlo method then rigorously satisfies the bound 01 t W  without artificially truncating numerical solutions.…”

Section: Parameter Identification Of the Growth Modelmentioning

confidence: 99%

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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

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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.

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“…We can use numerical schemes to simulate bounded numerical solutions inheriting this property [52], further supporting usefulness of the proposed model in applications.…”

Section: ( ) ( )supporting

confidence: 52%

Section: Parameter Identification Of the Growth Modelmentioning

confidence: 99%

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

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“…We propose the following version of the semi-discrete method for the approximation of (2), (14) yt n+1 = ∆W n + ytn + (∆W n + ytn ) 2 + 4(1 + b∆)a∆ 2(1 + b∆) ,…”

Section: Letmentioning

confidence: 99%

Lamperti Semi-Discrete method

Halidias,

Stamatiou

2021

Preprint

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We study the numerical approximation of numerous processes, solutions of nonlinear stochastic differential equations, that appear in various applications such as financial mathematics and population dynamics. Between the investigated models are the CIR process, also known as the square root process, the constant elasticity of variance process CEV, the Heston 3/2-model, the Aït-Sahalia model and the Wright-Fisher model. We propose a version of the semi-discrete method, see [1], which we call Lamperti semidiscrete (LSD) method. The LSD method is domain preserving and seems to converge strongly to the solution process with order 1 and no extra restrictions on the parameters or the step-size.

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“…Schurz also discussed the convergence and stability of the balanced methods for stochastic biological models in [3]. Recently, Stamatiou [4] studied the semi‐discrete method to preserve positivity of the Wright–Fisher model. Halidias [5] constructed positivity preserving numerical schemes for the two‐factor Cox–Ingersoll–Ross model in finance.…”

Section: Introductionmentioning

confidence: 99%

A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations

Tan

Mayavel

Rathinasamy

et al. 2020

Numerical Methods Partial

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In a previous paper, a numerical method preserving positivity was constructed for stochastic age‐dependent population equations. However, only the local error of the balanced Euler method was verified. In this paper, we will give the global error of this numerical method in the mean square sense. Moreover, the strong convergence order is investigated which proves the convergence of the aforementioned method with strong order p=12 in the mean of global error. At last, we give some numerical experiments to illustrate the efficiency of our method.

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A boundary preserving numerical scheme for the Wright–Fisher model

Cited by 15 publications

References 14 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

Lamperti Semi-Discrete method

A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations

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