MIT OpenCourseWare

Browse materialsMIT 15.070J · Fall 2013

Advanced Stochastic Processes

Subjects: Management · Statistics

Art: Gaston, John, (John Gaston merchant ledger) - DPLA -…, 1773 · Public domain

Instructor: Prof. David Gamarnik
Term: Fall 2013
Level: Graduate
What's inside: 5 solutions · 1 lecture note · 1 reading · 28 other files · 4 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 15.070J Advanced Stochastic Processes, Fall 2013, Prof. David Gamarnik — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Has MIT solutions 5 files in this course are named by MIT as solutions.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Probability: Theory and Examples · Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

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Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes

22 files

Assignments

8 files

Exams

Other materials from this course

MIT OpenCourseWare, Prof. David Gamarnik, 15.070J Advanced Stochastic Processes, Fall 2013.

License: CC BY-NC-SA 4.0 · Edition: Fall 2013 · Open the original course on OCW ↗

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Advanced Stochastic Processes

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Exams

Other materials from this course

Lecture 1: Metric spaces and topology

Lecture 2: Large deviations for i.i.d. random variables

Lecture 3: Large deviations theory Cramér’s theorem

Lecture 4: Applications of the large deviations technique

Lecture 5: Extension of LD to ℝdand dependent process Gärtner-Ellis theorem

Lecture 6: Introduction to Brownian motion

Lecture 7: The reflection principle The distribution of the maximum Brownian motion with drift

Lecture 8: Quadratic variation property of Brownian motion

Lecture 9: Conditional expectations, filtration and martingales

Lecture 10: Martingales and stopping times I

Lecture 11: Martingales and stopping times II Martingale convergence theorem

Lecture 12: Martingale concentration inequalities and applications

Lecture 13: Concentration inequalities and applications

Lecture 14: Introduction to Ito calculus

Lecture 15: Ito integral for simple processes

Lecture 16: Definition and properties of Ito integral

Lecture 17: Ito process Ito formula

Lecture 18: Integration with respect to martingales

Lecture 19: Applications of Ito calculus to financial economics

Lecture 20: Introduction to the theory of weak convergence

Lecture 21: Functional law of large numbers Construction of the Wiener measure

Lecture 22: Skorokhod mapping theorem Reflected Brownian motion