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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Poisson Point Processes and Their Application to Markov Processes

Poisson Point Processes and Their Application to Markov Processes

Itô, Kiyosi
Watanabe, Shinzo
Shigekawa, Ichiro

Paperback

Series: Springerbriefs in Probability and Mathematical Statistics, Book 1

General MathematicsProbability & Statistics

ISBN10: 9811002711
ISBN13: 9789811002717
Publisher: Springer Nature
Published: Feb 1 2016
Pages: 43
Weight: 0.20
Height: 0.12 Width: 6.14 Depth: 9.21
Language: English
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m

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