# Stochastic Processes

Stochastic Process as taught in Durett's Book in STAT650.

## Markov Chains

## Poisson Processes

The following 3 definitions of the Poisson process are equivalent.

- A Poisson process with rate is a counting process where the number of arrivals in a given time period has distribution
- A Poisson process is a renewal process with rate
- A Poisson process is a continuous time markov chain with and