Limit Behaviour for Stochastic Monotonicity and Applications.

Abstract

A transition probability function P is said to be stochastically monotone if P(x,-ALPHA,Y) is non-increasing in x for every fixed y. A (non-homogeneous) Markov chain or process is said to be stochastically monotone if its transition probability functions are stochastically monotone. Diffusions, random walks, birth-and-death and branching processes are examples of such models. It is shown that stochastically monotone processes exhibit two basic types of asymptotic behaviour. Chains with stationary transition probabilities display a cyclic pattern, and a suitably normed and centered chain turns out to converge almost surely if its is geometrically growing. Applications to diffusions and branching processes are added.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1985
Accession Number
ADA153814

Entities

People

  • H. Cohn

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Classification
  • Continuity
  • Convergence
  • Diffusion
  • Distribution Functions
  • Ergodic Processes
  • Intervals
  • Markov Chains
  • Markov Processes
  • Normal Distribution
  • North Carolina
  • Numbers
  • Probability
  • Random Variables
  • Stationary
  • Stochastic Processes
  • Transitions

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.