Smoluchowski方程及其扩散过程的自然边界
Natural boundaries for the Smoluchowski equation and affiliated diffusion processes
摘要：
从输入输出统计数据推导微观动力学的薛定谔问题已知可以用马尔可夫扩散来解决。解决方案的唯一性被发现链接到自然边界尊重的基础随机运动。通过选择一个参考Smoluchowski扩散过程，我们自动固定Feynman-Kac势和它引起的局部加速度场。我们产生家庭的附属扩散相同的本地动态，但不同的不可达的有限，半无限和无限域上的边界。对于每个扩散过程的唯一Feynman-Kac核得到的约束（Dirichlet边界数据）的Wiener路径integration.As一个副产品的讨论，我们给出了一个概述的问题的不可访问的边界的扩散和汇集（有时从意想不到的角度来看）的结果是鲜为人知的，分散在出版物几乎没有沟通的数学和物理领域。
英文摘要：
The Schrödinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion. By choosing a reference Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential and the field of local accelerations it induces. We generate the family of affiliated diffusions with the same local dynamics, but different inaccessible boundaries on finite, semi-infinite and infinite domains. For each diffusion process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet boundary data) Wiener path integration.As a by-product of the discussion, we give an overview of the problem of inaccessible boundaries for the diffusion and bring together (sometimes viewed from unexpected angles) results which are little known, and dispersed in publications from scarcely communicating areas of mathematics and physics.
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。
