扩散过程的漂移与连分数
Excursions of diffusion processes and continued fractions
摘要：
众所周知，一维扩散过程的漂移可以通过考虑与该过程相关联的某个Riccati方程来研究。我们表明，在许多情况下的利益，Riccati方程可以解决的无限连分数。我们研究的概率意义的扩展。为了说明我们的结果，我们讨论了在确定性和随机环境中的扩散的一些例子。
英文摘要：
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.
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。
