# MA 783 - Advanced Stochastic Processes-Fall 2022

### Instructor: Konstantinos Spiliopoulos

Office: 111 Cummington Street, Room MCS233D

Office Hours: Tuesday and Thursday 12:30-13:30.

Email: kspiliop_at_math.bu.edu

*to send me an email replace _at_ by @.*

### Meets:

TuTh... 11:00-12:15 at CAS 314

** Texts:**
*An Stochastic differential equations*, Oksendal, B. Springer Berlin Heidelberg, 2003.

** Recommended Texts:**

*An Stochastic differential equations*, Oksendal, B. Springer Berlin Heidelberg, 2003.
*Brownian motion and stochastic calculus*, Karatzas I., Shreve S., Springer 2012.
*Stochastic Processes*, Bass, RF., Cambridge University Press, 2011.

We will combine many different sources, including selections from textbooks and research articles.

**Course Description:** Proof-based approach to stochastic processes. Topics may include: Sigma algebra, filtrations, optional sampling theorems, stopping times, martingale theory, Markov
processes, Brownian motion, Poisson processes, stochastic integral and related properties, stochastic differential equations, Ito formula, calculus for semimartingales, Markov property, connections to partial differential equations, Fokker-Planck equation.

**Prerequisites:** MA 779 and MA 780, Probability Theory I and II, or their
equivalents; or consent of instructor. The students are required to have a solid understanding of graduate level probability and calculus.

I will try to follow the syllabus as closely as possible. However it may change depending on our progress.
Any changes will be announced in class and posted here.

*Homework assingments:*

Assingment | Due Date | Assignment | Material Covered |

*Currently the Exam schedule is as follows:*

Date | Assignment | Material Covered |

TBA | Midterm | TBA |

TBA | Final | TBA |

**Tentative grading policy:**
Your grade will be based on :(a) Homework (55%), (b) midterm exam (20%) and final exam (25%). The grading
policy may change depending on the progress of the class.

**Exam & Homeworks:**

**Exams: ** There will be one midterm exam and one final exam. The exam material for each one of the two exams will be announced in class and posted on the webpage of the course.

** Homeworks: ** There will be several homeworks, both theoretical and more of applied flavor.
The due date of each homework will be announced in class and it will usually be 7-10 days after.
The lowest homework will be dropped if you participate in class. Late homeworks will NOT be accepted.

**Make-up policy:**
Make up exams will be given only in extreme circumstances, and only when
accompanied by appropriate documentation. Any student with a valid reason to be given a make up
exam must contact me prior to the exam, either by email or in person, and present documentation
at the next class session attended.