Stochastic systems courses

This page collects some information about stochastic systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on the current stochastic systems sequence (ACM/EE 116, ACM 216, ACM 217/EE 164).

Additional stochastic systems courses at Caltech

The following table lists all of the courses that I was able to find that have been taught in the last four years. Enrollments (when given) are for 2005-2008, based on data from the registrar.

Course	enroll	2005-06	2006-07	2007-08	2008-09
ACM/EE 116 - Introduction to Stochastic Processes and Modeling	30-50	Owhadi	Owhadi	Owhadi	Owhadi
ACM/ESE 118 - Methods in Applied Statistics and Data Analysis	40-50	Schneider	Schneider	Tropp	Candes
ACM 216 - Markov Chains	15-20	Owhadi	Owhadi	Candes	Owhadi
ACM 217 - Advanced Topics in Stochastic Analysis	2-12	Owhadi	Von Handel	Hassibi	N/O
ACM 257 - Special Topics in Financial Mathematics	20	N/O	Hill	N/O	N/O

Course listings

The course listings below are from the Caltech catalog, mainly to serve as a reference for the rest of the information on this page.

ACM/EE 116. Introduction to Stochastic Processes and Modeling. 9 units (3-0-6); first term. Prerequisite: Ma 2 ab or instructor’s permission.Introduction to fundamental ideas and techniques of stochastic analysis and modeling. Random variables, expectation and conditional expectation, joint distributions, covariance, moment generating function, central limit theorem, weak and strong laws of large numbers, discrete time stochastic processes, stationarity, power spectral densities and the Wiener-Khinchine theorem, Gaussian processes, Poisson processes, Brownian motion. The course develops applications in selected areas such as signal processing (Wiener filter), information theory, genetics, queuing and waiting line theory, and finance.

ACM/ESE 118. Methods in Applied Statistics and Data Analysis. 9 units (3-0-6); first term. Prerequisite: Ma 2 or another introductory course in probability and statistics. Introduction to fundamental ideas and techniques of statistical modeling, with an emphasis on conceptual understanding and on the analysis of real data sets. Multiple regression: estimation, inference, model selection, model checking. Regularization of ill-posed and rank-deficient regression problems. Cross-validation. Principal component analysis. Discriminant analysis. Resampling methods and the bootstrap.

ACM 216. Markov Chains, Discrete Stochastic Processes and Applications. 9 units (3-0-6); second term. Prerequisite: ACM/EE 116 or equivalent. Stable laws, Markov chains, classification of states, ergodicity, von Neumann ergodic theorem, mixing rate, stationary/equilibrium distributions and convergence of Markov chains, Markov chain Monte Carlo and its applications to scientific computing, Metropolis Hastings algorithm, coupling from the past, martingale theory and discrete time martingales, rare events, law of large deviations, Chernoff bounds.

ACM 217. Advanced Topics in Stochastic Analysis. 9 units (3-0-6); third term. Prerequisite: ACM 216 or equivalent. The topic of this course changes from year to year and is expected to cover areas such as stochastic differential equations, stochastic control, statistical estimation and adaptive filtering, empirical processes and large deviation techniques, concentration inequalities and their applications. Examples of selected topics for stochastic differential equations include continuous time Brownian motion, Ito’s calculus, Girsanov theorem, stopping times, and applications of these ideas to mathematical finance and stochastic control. Not offered 2008–09.

ACM 257. Special Topics in Financial Mathematics. 9 units (3-0-6); third term. Prerequisite: ACM 95/100 or instructor’s permission. A basic knowledge of probability and statistics as well as transform methods for solving PDEs is assumed. This course develops some of the techniques of stochastic calculus and applies them to the theory of financial asset modeling. The mathematical concepts/tools developed will include introductions to random walks, Brownian motion, quadratic variation, and Ito-calculus. Connections to PDEs will be made by Feynman-Kac theorems. Concepts of risk-neutral pricing and martingale representation are introduced in the pricing of options. Topics covered will be selected from standard options, exotic options, American derivative securities, term-structure models, and jump processes. Instructor: Hill.