AI 中文总结
研究具有泊松随机测度的随机比例延迟模型，采用补偿分步θ技术，证明其数值格式收敛且具有几乎必然指数稳定性，并通过数值例子验证理论结果。
AI 中文摘要
近年来，随机比例延迟模型受到广泛关注，并应用于金融、生物、控制和随机神经网络等不同领域。在研究随机微分方程时纳入跳跃也更可取。本文研究了具有泊松随机测度的随机比例延迟模型，将补偿分步θ技术应用于该模型。该数值格式具有非发散性，在后续假设下收敛到模型解。此外，利用离散半鞅收敛定理研究了数值格式的几乎必然指数稳定性。最后，通过一些数值例子验证了理论结果。
英文摘要
Recently, stochastic pantograph models have gained an intensive attention and have been used in different fields such as finance, biology, control and stochastic neural networks. It is also more preferable to incorporate jumps during the study of stochastic differential equations. In this paper, stochastic pantograph model with Poisson random measure is studied. The compensated split-step theta technique is applied to the considered model. The numerical scheme exhibits a non divergent attitude and converges to the solution of our model under assumptions addressed later on. Furthermore, the almost sure exponential stability of the numerical scheme is investigated via utilizing the discrete semi-martingale convergence theorem. Finally, theoretical findings are manifested via some numerical examples.
