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Knotting of One-Dimensional Feller Processes

✍ Scribed by H. Langer; W. Schenk

Publisher
John Wiley and Sons
Year
1983
Tongue
English
Weight
481 KB
Volume
113
Category
Article
ISSN
0025-584X

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✦ Synopsis

I n the papers [l, 21 B. I. KOPYTKO considered the following problem of "knotting" two one-dimensional diffusions : Given two differential operators on intervals I , : = (-cm, T ) , I, : = (r, m), respectively, which (after imposing a boundary condition a t r ) "generate" diffusion processes on the closures 1, and I,, respectively.

How to describe the most general Feller process with continuous trajectories on ( -0 0 , cm) which on I i is "given" by the above operator Ai, i = 0, 1. B. I. KOPYTKO solved this problem using results on parabolic differential equations with non-continuous coefficients. He showed that the infinitesimal generators of these FELLER processes are given by A,, A, and a "knotting condition" at r. This

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