Week | Lecture Notes |

1 | Introduction & Course Objectives |

2 | Review of Probability |

3 | Conditional Prob & Markov Chains I |

4 | Measure Theory Review |

5 | Random Walks & Hitting Probabilities |

6 | RW, Hitting Probabilities, & SPRT |

7 | Poisson Birth/Death |

8 | Brownian Motion |

9 | Brownian Bridge |

10 | Continuous-Time Markov Chains |

11 | Martingle Methods |

12 | Martingales & Optional Sampling |

14 | Martingales Applications |

| Final Projects |