一类与Ornstein-Uhlenbeck过程有关的非线性随机游动
A class of nonlinear random walks related to the Ornstein-Uhlenbeck process
摘要：
与马尔可夫过程理论相反，对于所谓的非线性马尔可夫过程，没有一般的理论存在。我们研究了一个与经典概率论有关的“非线性马尔可夫过程”的例子，仅仅是随机游动。这个模型提供了有趣的现象（缺乏在经典的马尔可夫链）：连续的平稳措施，守恒量，收敛到平稳的经典随机游动等。
英文摘要：
Contrary to the theory of Markov processes, no general theory exists for the so called nonlinear Markov processes. We study an example of "nonlinear Markov process" related to classical probability theory, merely to random walks. This model provides interesting phenomena (absent in classical Markov chains): continuum of stationary measures, conserved quantities, convergence to stationary classical random walks etc.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
