发表机构
University of Mannheim（曼海姆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对依赖分布的随机Volterra方程，在不同假设下推导强解的稳定性估计与收敛定理，还证明了相关Volterra局部鞅问题解的稳定性，为这类方程的稳定性分析提供了理论结果。
AI 中文摘要
我们研究依赖分布的随机Volterra方程关于系数、Volterra核和初值变化的稳定性性质。在系数满足Lipschitz连续性假设下，我们首先得到强解的定量稳定性估计，给出显式误差界；随后在弱得多的假设下证明强解的一般收敛定理，将Lipschitz连续性替换为连续性假设及近似序列的一致线性增长；最后研究相关的依赖分布的Volterra局部鞅问题，证明在系数、核和初分布收敛时其解的稳定性。
英文摘要
We investigate stability properties of distribution-dependent stochastic Volterra equations with respect to changes in the coefficients, the Volterra kernels, and the initial condition. Under Lipschitz continuity assumptions on the coefficients, we first derive quantitative stability estimates for strong solutions with explicit error bounds. We then prove a general convergence theorem for strong solutions under substantially weaker assumptions, replacing Lipschitz continuity by a continuity assumption together with uniform linear growth of the approximating sequence. Finally, we study the associated distribution-dependent Volterra local martingale problem and prove the stability of its solutions under convergence of the coefficients, kernels, and initial distributions.
