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

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