Application of p-Adic analysis methods in describing Markov processes on ultrametric spaces isometrically embedded into ?sub class="a-plus-plus"> p

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• 作者：A. Kh. Bikulov ; A. P. Zubarev
• 关键词：p ; adic analysis ; Markov processes ; ultrametric spaces ; isometric embedding
• 刊名：P-Adic Numbers, Ultrametric Analysis, and Applications
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：7
• 期：2
• 页码：121-132
• 全文大小：589 KB
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• 作者单位：A. Kh. Bikulov (1)
  A. P. Zubarev (2) (3)
  
  1. Institute of Chemical Physics, Kosygina Street 4, 117734, Moscow, Russia
  2. Physics Department, Samara State Aerospace University, Moskovskoe shosse 34, 443123, Samara, Russia
  3. Physics and Chemistry Department, Samara State University of Railway Transport, Perviy Bezimyaniy pereulok 18, 443066, Samara, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：2070-0474

文摘

We propose a method for describing stationary Markov processes on the class of ultrametric spaces \(\mathbb{U}\) isometrically embedded in the field ?sub> p of p-adic numbers. This method is capable of reducing the study of such processes to the investigation of processes on ?sub> p . Thereby the traditional machinery of p-adic mathematical physics can be applied to calculate the characteristics of stationary Markov processes on such spaces. The Cauchy problem for the Kolmogorov-Feller equation of a stationary Markov process on such spaces is shown as being reducible to the Cauchy problem for a pseudo-differential equation on ?sub> p with non-translation-invariant measure m(x) d _p x. The spectrum of the pseudo-differential operator of the Kolmogorov-Feller equation on ?sub> p with measure m(x) d _p x is found. Orthonormal basis of real valued functions for L 2 (?sub> p ,m(x) d _p x) is constructed from the eigenfunctions of this operator.