ON THE MCKEAN-VLASOV LIMIT FOR INTERACTING DIFFUSIONS
ON THE MCKEAN-VLASOV LIMIT FOR INTERACTING DIFFUSIONS
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DOI：
10.1002/mana.19881370116
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发表时间：
1988-01-01
影响因子：
1
通讯作者：
GARTNER, J
中科院分区：
文献类型：
--
作者：
GARTNER, J
对于具有长程弱相互作用的Rd区域中的扩散系统，研究了相关经验过程的行为。在关于漂移系数和扩散系数的温和增长和光滑性假设下，如单调性和单调性条件下，证明了大数定律和混沌的传播。研究了McKean ‐ Vlasov方程弱解的存在唯一性及相应的非线性鞅问题.
For a system of diffusions in a domain ofRdwith long‐range weak interaction the behavior of the associated empirical process is studied. Under mild growth and smoothness assumptions on the drift and diffusion coefficients such as coercivity and monotonicity conditions the law of large numbers and the propagation of chaos are proved. Existence and uniqueness of the weak solution to the McKean ‐ Vlasov equation and the associated non‐linear martingale problem are investigated.