论文标题
由LévyNoise驱动的McKean-Vlasov方程的良好的和驯服的欧拉计划
Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise
论文作者
论文摘要
我们证明，在轻度假设下，尤其是不需要有限的Lévy量度，在轻度假设下驱动的McKean-Vlasov随机微分方程的解决方案的解决方案具有良好的作用。允许漂移，扩散和跳跃系数是随机的，可以在状态变量中超级线性生长，所有这些都可能取决于溶液过程的边际定律。在放松条件下，我们比文献中存在的混乱结果传播了混乱的结果，并且与我们的体重良好的结果一致。 我们为关联的相互作用粒子系统提出了一种驯服的欧拉方案，并证明其强收敛速度是任意接近$ 1/2 $的。作为一种副产品，我们还获得了有关良好性，混乱传播的相应结果，以及McKean-Vlasov随机延迟差分方程（SDDE）和McKean-Vlasov随机差分方程的驯服Euler方案的强烈融合，并获得了Markovian Switching（Sdewms），由Markovian Switching（Sdewms），两者都受到驱动的噪声。此外，即使是由Lévy噪声和超线性增长系数驱动的普通SDE，我们对驯服Euler方案的结果也是新的。
We prove the well-posedness of solutions to McKean-Vlasov stochastic differential equations driven by Lévy noise under mild assumptions where, in particular, the Lévy measure is not required to be finite. The drift, diffusion and jump coefficients are allowed to be random, can grow super-linearly in the state variable, and all may depend on the marginal law of the solution process. We provide a propagation of chaos result under more relaxed conditions than those existing in the literature, and consistent with our well-posedness result. We propose a tamed Euler scheme for the associated interacting particle system and prove that the rate of its strong convergence is arbitrarily close to $1/2$. As a by-product, we also obtain the corresponding results on well-posedness, propagation of chaos and strong convergence of the tamed Euler scheme for McKean-Vlasov stochastic delay differential equations (SDDE) and McKean-Vlasov stochastic differential equations with Markovian switching (SDEwMS), both driven by Lévy noise. Furthermore, our results on tamed Euler schemes are new even for ordinary SDEs driven by Lévy noise and with super-linearly growing coefficients.
