**Important Dates: **Last day for Automatic Withdrawal: Wednesday, March 7. Exam 1: Monday, February 13. Exam 2: Monday, March 26. Final Exam: 5-7 p.m., Monday, April 30.

** Religious Holiday Policy:** If you will miss class, especially a class during which there will be an exam or other required work, for a religious holiday, you must inform me during the first two weeks of the semester.

**Cheating:** It is not possible to cheat on homeworks. All exams must be your own individual work. All suspected cases of cheating will be handled in accordance with University procedures found at http://dsa.indiana.edu/ethics.html . If you do cheat, you will receive an F* in the course - the star informs the registrar that the F is due to cheating. Additional sanctions may be imposed by the Dean.

** Homework:** There will be 10 homework assignments throughout the term. See the schedule below. A star (*) on a problem indicates that a hint to the problem appears in the back of the text. At least one assignment will be dropped from the calculation for your homework average.

** Grades:** Grades are calculated as 40% Homework, 15% Exam 1, 15% Exam 2, 25% Final Exam, 5% Attendance and Participation. In the rare event that a student who has failed to turn in their homeworks consistently on time performs extraordinarily well (as in nearly perfectly) on the in-class exams, an alternative weighting will be used that discounts the homework contribution to the course grade.

## Tentative Syllabus | ||
---|---|---|

Date | Lecture Topics | Section |

Monday, January 9 | Poisson point processes (through Thm 23.1) | Section 23 |

Wednesday, January 11 | Poisson point processes (through condition 3) | Section 23 |

Friday, January 13 | Poisson point processes (condition 4 and stochastic processes) | Section 23 |

Homework 1: (due Friday, Jan. 20) 23.3*, 23.4*, 23.9*, 23.10 (read 23.11 for an application, but it is not assigned to turn in) | ||

Monday, January 16 | Martin Luther King Jr. Holiday | -- |

Wednesday, January 18 | Weak convergence (through Thm 25.4) | Section 25 |

Friday, January 20 | Fundamental theorems | Section 25 |

Monday, January 23 | Helly's theorem and integration to the limit review | Section 25 |

Wednesday, January 25 | Characteristic functions | Section 26 |

Friday, January 27 | Inversion and uniqueness | Section 26 |

Homework 2: (due Monday, January 30) 25.4, 25.17, 25.18, 25.20* | ||

Monday, January 30 | Continuity theorem | Section 26 |

Wednesday, February 1 | Central Limit Theorem (easy case) | Section 27 |

Friday, February 3 | Lindenberg and Lyapounov Theorems | Section 27 |

Homework 3: (due Monday, February 6) 26.1* 26.20, 26.21, 27.1 | ||

Monday, February 6 | Multivariate analogs - limit theorems | Section 29 |

Wednesday, February 8 | Multivariate analogs - Central Limit Theorem | Section 29 |

Friday, February 10 | Selected topics on derivatives on the line | Section 31 |

| ||

Monday, February 13 | Exam 1 (Covering through the easy version of the Central Limit Theorem) | |

Wednesday, February 15 | Signed measures | Section 32 |

Friday, February 17 | Radon-Nikodym Theorem | Section 32 |

Homework 4: (due Monday, February 20) 27.4, 27.5, 27.10, 29.2 | ||

Monday, February 20 | Conditional probabilities | Section 33 |

Wednesday, February 22 | Conditional probabilities | Section 33 |

Friday, February 24 | Conditional probabilities | Section 33 |

Homework 5: (due Monday, February 27) 29.12, 29.13, 31.1, 31.2 | ||

Monday, February 27 | Conditional expectation | Section 34 |

Wednesday, February 29 | Conditional expectation | Section 34 |

Friday, March 2 | Martingales: definitions and examples | Section 35 |

Homework 6: (due Monday, March 5) 32.4, 33.3*, 33.5(a), 33.8 | ||

Monday, March 5 | Submartingales and gambling | Section 35 |

Wednesday, March 7 | Stopping times | Section 35 |

Friday, March 9 | Convergence theorems | Section 35 |

March 10-18 Spring Break | ||

Homework 7: (due Monday, March 19) 34.3*, 34.4*, 34.6, 34.11* | ||

Monday, March 19 | Applications of martingales | Section 35 |

Wednesday, March 21 | Applications of martingales | Section 35 |

Friday, March 23 | Stochastic processes and review | Section 36 |

| ||

Monday, March 26 | Exam 2 (Covering through martingales) | |

Wednesday, March 28 | Kolmogorov's Existence Theorem | Section 36 |

Friday, March 30 | Inadequacies | Section 36 |

Homework 8: (due Monday, April 2) 35.2, 35.4*, 35.5, 35.6 | ||

Monday, April 2 | Brownian motion | Section 37 |

Wednesday, April 4 | Continuity of paths | Section 37 |

Friday, April 6 | Measurability, irregularity, scaling properties | Section 37 |

Homework 9: (due Friday, April 13) 36.2, 36.7*, 37.1*, 37.2 | ||

Monday, April 9 | Set of zeros | Section 37 |

Wednesday, April 11 | Strong Markov property | Section 37 |

Friday, April 13 | Reflection principle | Section 37 |

Monday, April 16 | Invariance | Section 37 |

Wednesday, April 18 | Harmonic functions and Brownian motion (supplemental) | Section 37 |

Friday, April 20 | Harmonic functions and Brownian motion (supplemental) | Section 37 |

Homework 10: (due Monday, April 23) 37.11, 37.12, 37.13, 37.14* | ||

Monday, April 23 | Supplemental topics on Brownian motion | Section 37 |

Wednesday, April 25 | Supplemental topics on Brownian motion | Section 37 |

Friday, April 27 | Summary and evaluations | |

Final Exam: Monday, April 30 5-7 pm in BH 246 |