具有跳跃过程的随机比例延迟Mckean-Vlasov模型的截断Euler-Maruyama算法的收敛性和稳定性
Convergence and stability of truncated Euler-Maruyama algorithm for stochastic proportional delay Mckean-Vlasov models with jump process
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中文总结 AI 辅助
研究具有跳跃过程的随机比例延迟Mckean-Vlasov模型，应用截断Euler-Maruyama算法，探讨其收敛速度和几乎必然指数稳定性，并通过数值例子支持理论分析。
中文摘要 AI 辅助
随机Mckean-Vlasov模型在金融、生物学和控制等不同领域具有重要意义。本文关注具有Lévy跳跃的随机比例延迟Mckean-Vlasov模型，其非跳跃系数允许超出线性增长。应用截断Euler-Maruyama算法到该模型，研究上述数值算法的收敛速度和几乎必然指数稳定性。最后给出数值例子以支持理论分析。
英文摘要
Stochastic Mckean-Vlasov models have a substantial importance in different fields such as finance, biology and control. This paper puts the light on stochastic proportional delay Mckean-Vlasov model with Lévy jump where the non-jump coefficients are granted the permission to grow beyond linearity. The truncated Euler-Maruyama algorithm is then applied to our addressed model where the convergence rate and almost sure exponential stability of the aforementioned numerical algorithm are being investigated. Finally, numerical examples are presented to foster the theoretical analysis done throughout the paper
