MAE 271B

Stochastic Estimation MAE 271B (Winter 2026 @ UCLA)

An introduction to stochastic processes, stochastic calculus, and estimation theory, with an emphasis on continuous-time filtering. The course covers stochastic (Itô) calculus, continuous-time Gauss–Markov systems, the continuous-time Kalman filter, stationarity, power spectral density, and the Wiener filter, followed by a selection of results from estimation theory including the continuous-time colored-noise filter. Time permitting, the extended Kalman filter and the particle filter are introduced.

Instructor's bio: Shahriar Talebi is an Assistant Professor in the Department of Mechanical & Aerospace Engineering at the UCLA Samueli School of Engineering (since July 2025). Before UCLA, he was a Postdoctoral Research Fellow at Harvard University and a contributor to the NSF AI Institute in Dynamic Systems (Dynamics AI). He received a Ph.D. in control theory from the University of Washington in 2023—focusing on constrained decision-making and control in complex systems—and an M.Sc. in Mathematics (differential geometry) from UW.

Course Logistics

  • Instructor: Dr. Shahriar Talebi, s.talebi@ucla.edu, office: Eng IV, 38-137F
  • Lectures: Mondays & Wednesdays, 10:00am–11:50am
  • Class Location: Boelter Hall 5272
  • Office Hours: Mondays & Wednesdays 12:00pm–1:00pm (or by arrangement)

Main Textbook

  1. Jason L. Speyer and Walter Chung, Stochastic Processes, Estimation, and Control, SIAM, 2008.

Additional Resources

  1. Ramon van Handel, Stochastic Calculus, Filtering, and Stochastic Control, Lecture Notes, 2007.
  2. Bernt Øksendal, Stochastic Differential Equations, Springer-Verlag, Sixth Edition, 2003.
  3. Ioannis Karatzas and Steven Shreve, Brownian Motion and Stochastic Calculus, Second Edition, 1991.
  4. Rick Durrett, Probability: Theory and Examples, Fifth Edition, 2019.

Learning Objectives

This course covers material mostly from Chapters 5 through 8 of Speyer & Chung '08:

  • Chapter 5 — Stochastic Processes and Stochastic (Itô) Calculus
  • Chapter 6 — Continuous-Time Gauss–Markov Systems: Continuous-Time Kalman Filter, Stationarity, Power Spectral Density, and the Wiener Filter
  • Chapter 8 — A Selection of Results from Estimation Theory: Section 8.1, Continuous-time colored-noise filter
  • Additional topics (if time permits): Chapter 7 — The Extended Kalman Filter, Particle Filter

Lecture Notes — Table of Contents

Table of Contents
Lecture Topic Notes
1 Introduction to Brownian Motion: motivation and the random-walk construction PDF
2 Review of probability spaces: σ-algebras, measurability, and probability measures PDF
3 Modes of convergence of random variables (a.s., in probability, in Lp, in law) PDF
4 Conditional expectation and its properties PDF
5 The Wiener process: definition and basic properties PDF
6 The Wiener process (cont.): martingale and Markov properties PDF
7 Construction of the Itô integral PDF
8 Properties of the Itô integral: martingale property and maximal inequality PDF
9 Itô's formula (Itô calculus) PDF
10 Stochastic differential equations (SDEs) and examples PDF
11 Existence, uniqueness, and the Markov property of SDE solutions PDF
12–14 The filtering problem: the projection theorem and the innovations process PDF
15–16 The Kalman–Bucy filter: scalar and multi-dimensional linear filtering PDF

Videos

The recorded lectures from MAE 271B in Winter 2021, taught by Prof. Jason Speyer, will also be made available on the course website before each class and are expected to be viewed beforehand. In-class time will be used to discuss the lecture material, answer questions, and work through problems/papers.

Grading

  • Midterm Exam — 40%
  • Project Presentation and Final — 60%