Advertisement

On delay and asymmetry points of one-dimensional diffusion processes

  • B. P. Harlamov
Article
  • 20 Downloads

A homogeneous second order linear differential equation is considered. On an open interval where the equation has sense, it generates a family of operators of the Dirichlet problem on the set of all subintervals; this family is a generalized semi-group. Let the equation be defined on two disjoint intervals with a common boundary point z. It is shown that an extension of the corresponding two semi-groups of operators to the semi-group of operators corresponding to the union of the intervals and the point z is not unique and depends on two abritrary constants. To give an interpretation of these arbitrary constants, we use a one-dimensional locally Markov diffusion process with special properties of passage of the point z. One of these arbitrary constants determines the delay of the process at the point z, and the second one induces an asymmetry of the process with respect to z. The two extremal values of the latter constant, 0 and ∞, determine the reflection of the process from the point z when the process approaches the point from the left and right, respectively. Bibliography: 4 titles.

Keywords

Reflection Russia Differential Equation Mechanical Engineer Diffusion Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    E. Kamke, Differentialgleichungen. Losungsmethoden und Losungen, Leipzig (1959).Google Scholar
  2. 2.
    B. P. Harlamov, Continuous Semi-Markov Processes, ISTE & Wiley, London (2008).MATHCrossRefGoogle Scholar
  3. 3.
    B. P. Harlamov, “Diffusion process with delay at ends of a segment,” Zap. Nauchn. Semin. POMI, 351, 284–297 (2007).Google Scholar
  4. 4.
    B. P. Harlamov, “On a Markov diffusion process with delayed reflection from ends of a segment,” Zap. Nauchn. Semin. POMI, 368, 231–255 (2009).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical EngineeringRASSt. PetersburgRussia

Personalised recommendations