#### Publication Date

1-9-1978

#### Abstract

In this dissertation we consider a model of a random walk, (Z_{n}}, on R(1) where the distribution of (Z_{n}} is dependent on a stochastic process (Y_{n}} and is given by g_{y}(z) where Y_{n-1} = y . Conditions on the environmental process (Y_{n}} are given for which transience or recurrence of the random walk (Z_{n}} can be detennined. The probability of n absorption and mean time problems are solved when (Y_{n}} is a finite Markov chain and (Z_{n}} is a classical random walk on the integer lattice.

#### Degree Name

Mathematics

#### Level of Degree

Doctoral

#### Department Name

Mathematics & Statistics

#### First Committee Member (Chair)

Robert Cogburn

#### Second Committee Member

Reuben Hersh

#### Third Committee Member

Richard J. Griego

#### Language

English

#### Document Type

Dissertation

#### Recommended Citation

Sanchez, Edwin Andrew. "A Random Walk in a Random Environment." (1978). https://digitalrepository.unm.edu/math_etds/134