Renewal Process

Regenerative Process

Stochastic Process Notes, from Lecture 10

1. Definition

A stochastic process $X(t)$ is a regenerative process if

• Process stochastically starts over at even time $S_1, S_2, \cdots$
• Times between events $X_1, X_2, \cdots$ are i.i.d

2. Regenerative Process v.s. Renewal Process

• A renewal process $N(t)$ counts (increasing over time) and has property 2 shown above.
• A regenerative process $X(t)$ keeps track of something else and starts over.

3. Example