Constructing Markov Processes with Random Times of Birth and Death,

Abstract

Given a time inhomogeneous Markov transition semigroup P(s/t) (x,dy) and an entrance rule m = (m sub t) satisfying m sub s P(s/t) < or = m sub t, Kuznetsov constructed a measure o sub m on path space so that the coordinate maps are Markovian with semigroup P (s/t) and so that the process is born according to the entrance rule m. Kuznetosov's approach was a Kolmogorov type construction. The authors give a new approach based on standard Markov process theory and a new analytic proof of the decomposition of m as: m sub t = v(- infinity/t) + integral from 0 to infinity of (s/t) p(ds), where p is a finite measure on R, and for each s, v superscript s = (vs/t) is an entrance law at s.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA171856

Entities

People

  • Joseph Glover
  • R. K. Getoor

Organizations

  • University of Florida

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Classification
  • Construction
  • Death
  • Decomposition
  • Distribution Functions
  • Markov Processes
  • Mathematics
  • Notation
  • Numbers
  • Probability
  • Rational Numbers
  • Security
  • Sequences
  • Standards
  • Theorems
  • Transitions

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space