Stochastic Age-dependent Population Equations Research Articles

Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay

We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ-method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switching. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.

Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps

This paper focuses on asymptotic mean-square boundedness of several numerical methods applied to a class of stochastic age-dependent population equations with Poisson jumps. The conditions under which the underlying systems are asymptotic mean-square boundedness are considered. It is shown that the asymptotic mean-square boundedness is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce asymptotic mean-square boundedness under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of asymptotic mean-square boundedness. Finally, an example is given for illustration.

Construction of positivity preserving numerical method for stochastic age-dependent population equations

The aim of this paper is to construct a numerical method preserving positivity for stochastic age-dependent population equations. We use the balanced implicit numerical techniques to maintain the nonnegative path of the exact solution. It is proved that the Balanced Implicit Method (BIM) preserves positivity and converges with strong order 1/2 under given conditions. Finally, two examples are simulated to verify the positivity and efficiency of the proposed method.

The existence and asymptotic behaviour of energy solutions to stochastic age-dependent population equations driven by Levy processes

In this paper, we introduce a class of stochastic age-dependent population equations driven by Levy processes. Existence and uniqueness of energy solutions for stochastic age-dependent population dynamic system are proved under Lipschitz condition in Hilbert space. The moment boundedness of the approximate solution by the Galerkin method is considered. We discuss by using the energy equality the exponential stability theorems of the energy solution to stochastic age-dependent population equations.

Convergence of the split-step θ-method for stochastic age-dependent population equations with Poisson jumps

In this paper, a new split-step θ (SSθ) method for stochastic age-dependent population equations with Poisson jumps is constructed. The main aim of this paper is to investigate the convergence of the SSθ method for stochastic age-dependent population equations with Poisson jumps. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory, the results show that the SSθ method has better accuracy compared to the Euler method.

Strong convergence of the split-stepθ-method for stochastic age-dependent population equations

In this paper, we constructed the split-step θ (SSθ)-method for stochastic age-dependent population equations. The main aim of this paper is to investigate the convergence of the SS θ-method for stochastic age-dependent population equations. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from the theory, and comparative analysis with Euler method is given, the results show the higher accuracy of the SS θ-method. Copyright © 2014 John Wiley & Sons, Ltd.

Asymptotic stability of stochastic age-dependent population equations with Markovian switching

The main aim of this paper is to discuss the almost surely asymptotic stability of the stochastic age-dependent population equations with Markovian switching. An example will be discussed to illustrate the theory.

Split-step [formula omitted]-methods for stochastic age-dependent population equations with Markovian switching

In this paper, a class of split-step θ -methods for solving stochastic age-dependent population equations with Markovian switching is constructed. The main aim of this paper is to investigate the convergence of the split-step θ -methods of stochastic age-dependent population equations with Markovian switching. It is proved that the split-step θ -methods converge to the analytical solutions of the equations under given conditions. An example is given for illustration.

Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion

Stochastic age-dependent population equations, one of the important classes of hybrid systems are studied. In general most equations of stochastic age-dependent population do not have explicit solutions. Thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the analytic solution. In the last section a numerical example is given.

Numerical analysis for stochastic age-dependent population equations with Poisson jump and phase semi-Markovian switching

In this paper, we shall examine the convergence of semi-implicit Euler approximation for stochastic age-dependent population equations with Poisson jump and phase semi-Markovian switching. Here, the main ideas from the papers Ronghua et al. (2009) [2] and Wang and Wang (2010) [3] are successfully developed to the more general cases. Finally, a numerical example is provided to illustrate the theoretical result of convergence.

Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps

We consider semi-implicit methods for stochastic age-dependent population equations with Poisson jumps. The main purpose of this paper is to show the convergence of the numerical approximation solution to the true solution with strong order p = 1 2 .

Convergence of numerical solutions to stochastic age-dependent population equations with Markovian switching

In this paper, a class of stochastic age-dependent population equations with Markovian switching is considered. The main aim of this paper is to investigate the convergence of the numerical approximation of stochastic age-dependent population equations with Markovian switching. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. An example is given for illustration.

Convergence of the semi-implicit Euler method for stochastic age-dependent population equations

A class of semi-implicit methods is introduced for stochastic age-dependent population equations. It is proved that the semi-implicit Euler methods are convergent with strong order p = 1 2 . An example is given to illustrate the efficiency of the semi-implicit Euler method.

Exponential stability of numerical solutions to stochastic age-dependent population equations

The main aim of this paper is to consider the exponential stability of the Euler–Maruyama scheme for a class of stochastic age-dependent population equation. The definition of exponential stability of numerical methods is established. The conditions under which the method is exponentially stable in mean square are determined.

Numerical analysis for stochastic age-dependent population equations with Poisson jumps

In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution.

Convergence of numerical solutions to stochastic age-dependent population equations

In this paper, stochastic age-dependent population equations, one of the important classes of hybrid systems, are studied. In general, most of stochastic age-dependent population equations do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the true solution.

Numerical analysis for stochastic age-dependent population equations

A numerical method proposed to approximate the solution of a class of stochastic age-dependent populations. We show that under certain conditions, weaker than Linear growth and Global Lips-chits, the Euler scheme applied to Stochastic age-dependent population, converges to the analytic solution, and provide information on the order of approximation.