Convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes

Strong convergence of the split-step θ-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion

“…Recently, the study of numerical methods for the stochastic age-dependent capital system has received a great deal of attention. For example, Zhang et al [1] discussed the exponential stability of Euler approximation for the stochastic age-dependent capital system with Poisson jumps, and further studied the convergence of Euler method for a class of stochastic age-dependent capital systems with random jump magnitudes and Markovian switching [2,3]. Subsequently, Zhang et al [4] constructed a split-step backward Euler (SSBE) method for stochastic age-dependent capital system with Markovian switching, and proved that the SSBE method converges with strong order of one half to the exact solution under the given conditions.…”

Convergence Analysis of Semi-Implicit Euler Methods for Solving Stochastic Age-Dependent Capital System with Variable Delays and Random Jump Magnitudes

“…Stochastic differential equations have been widely used to model the phenomena arising in many branches of science and industry fields such as biology, economic, finance, and ecology [1][2][3][4]. Recently, the numerical construction of stochastic age-dependent capital system has received a great deal of attention [5][6][7][8][9]. In [8], exponential stability of numerical solutions for a class stochastic age-dependent capital system with Poisson jumps was studied by Zhang et al in the case of deterministic magnitude.…”

“…In [8], exponential stability of numerical solutions for a class stochastic age-dependent capital system with Poisson jumps was studied by Zhang et al in the case of deterministic magnitude. Zhang and Rathinasamy [9] studied convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes, which extended the analysis in [8] to the case where the jump magnitudes are random. However, in many real problems, the capital systems can be modeled by stochastic dynamical systems whose evolutions depend not only on the current states, but also on their historical states.…”

“…Thus, numerical approximation schemes are invaluable tools for exploring its properties. There is a significant amount of literature that has been published concerning approximate schemes for stochastic differential equations with jumps [9][10][11] or stochastic differential delay equations [12][13][14]. In [15], Chalmers and Higham gave the semi-implicit Euler approximate solutions and proved the convergence of semi-implicit Euler methods under the Lipschitz condition.…”

Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion

“…Recently, the numerical construction of stochastic agedependent (vintage) capital system with standard Brownian motion has captured many researchers' attention. For example, Zhang et al [21,22] discussed the exponential stability of numerical solutions for the stochastic age-dependent capital system with Poisson jumps in the case of deterministic magnitude, and further studied the convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes. In their subsequent work [20], they constructed a split-step backward Euler method for stochastic age-dependent capital system with Markovian switching and proved that, under the one-sided local Lipschitz condition on the drift and local Lipschitz condition on the diffusion, the split-step backward Euler method converges with strong order of one half to the true solution.…”