Stochastic Process

This page contains resources about Stochastic Processes, Stochastic Systems, Random Processes and Random Fields.

More specific information is included in each subfield.

Subfields and Concepts
See Category:Stochastic Processes for some of its subfields.
 * Discrete-time Stochastic Processes
 * Continuous-time Stochastic Processes
 * State Space
 * Discrete
 * Continuous
 * Weak-sense Stationary Process / Wide-sense Stationary Process
 * Strictly Stationary Process / Strongly Stationary Process
 * Ergodicity / Ergodic Process
 * Mean-ergodic
 * Autocovariance-ergodic
 * Ergodic in the wide sense
 * Time domain
 * Autocorrelation Function
 * Frequency domain
 * Power Spectral Density / Power spectrum / Spectrum
 * Cramér Spectral Representation
 * Wold Decomposition Theorem / Wold Representation Theorem
 * Time Series Processes (Discrete-time and Continuous State Space)
 * Autoregressive (AR) Process
 * Moving Average (MA) Process
 * ARMA Process
 * Latent Variable Models (i.e. Partially Observed Probabilistic Models)
 * Continuous Latent Variable Models
 * Discrete Latent Variable Models
 * Stochastic Dynamical System
 * Random Dynamical System
 * Random Graphs
 * Random Fields
 * Markov Random Field / Markov Network
 * Gibbs Random Field
 * Gaussian MRF / Multivariate Gaussian distribution (not to be confused with Gaussian Random Field)
 * Gaussian Random Field
 * Markov Models
 * Discrete-time Markov Chain (Discrete-time and Discrete State Space)
 * Discrete-time Harris Chain (Discrete-time and Continuous State Space)
 * Continuous-time Markov Chain / Continuous-time Markov Process / Markov Jump Process
 * Continuous-time Stochastic Process with the Markov property (e.g. Wiener Process)
 * Hidden Markov Model
 * Markov Decision Process
 * Partially Observable Markov Decision Process
 * Hierarchical Markov Models
 * Gaussian Process
 * Gauss–Markov Process / AR Process
 * Ornstein-Uhlenbeck Process / Stationary Gauss–Markov Process
 * Wiener Process / Brownian Motion (Continuous-time and Continuous State Space)
 * Geometric Brownian Motion
 * Harmonic Process (e.g. Sinusoidal Model)
 * Innovations Process
 * Queues
 * Martingales
 * Jump Process
 * Point Process
 * Cox Point Process
 * Poisson Process
 * Dirichlet Process
 * Pitman–Yor Process
 * Chinese Restaurant Process
 * Indian Buffet Process
 * Lévy Process
 * Bernoulli Process
 * Pólya's Urn Process
 * Hoppe's Urn Process
 * Stick Breaking Process
 * Girsanov Transformation / Girsanov Theorem (in Probability Theory)
 * Stochastic Calculus (used in Computational Finance)
 * Itô Calculus
 * Itô's Lemma
 * Semimartingale

Video Lectures

 * Discrete Stochastic Processes by Robert Gallager

Lecture Notes

 * Stochastic Processes by Cosma Shalizi
 * Introduction to Stochastic Systems by Maxim Raginsky
 * Introduction to Stochastic Processes by Hao Wu
 * Advanced Stochastic Processes by David Gamarnik
 * Stochastic Systems by Florian Herzog
 * Stochastic Calculus by Jonathan Goodman
 * Stochastic Calculus by Michael R. Tehranchi
 * Stochastic Calculus by Fabrice Baudoin
 * Stochastic Calculus by Alan Bain

Books and Book Chapters
See Amazon and Google-Books for more books.
 * Hajek, B. (2015). Random Processes for Engineers. Cambridge University Press.
 * Pavliotis, G. A. (2014). Stochastic Processes and Applications. Springer.
 * Stark, H., Woods, J. W., Thilaka, B., & Kumar, A. (2012). Probability, statistics, and random processes for engineers. 4th Ed. Pearson.
 * Klebaner, F. C. (2012). Introduction to stochastic calculus with applications. 3rd Ed. Imperial College Press.
 * Papoulis, A., & Pillai, S. U. (2002). Probability, random variables, and stochastic processes. 4th Ed. Tata McGraw-Hill Education.
 * Gray, R. M. (2009). Probability, random processes, and ergodic properties. Springer Science & Business Media.
 * Stirzaker, D. (2005). Stochastic processes and models. Oxford University Press.
 * Grimmett, G., & Stirzaker, D. (2001). Probability and random processes. 3rd Ed. Oxford University Press.
 * Kao, E. P. (1997). An introduction to stochastic processes. Duxbury.
 * Ross, S. M. (1996). Stochastic processes. 2nd Ed. John Wiley & Sons.
 * Stark, H., & Woods, J. W. (1994). Probability, random processes, and estimation theory for engineers. Prentice Hall.
 * Helstrom, C.W., (1992). Probability and Stochastic Processes for Engineers. 2nd Ed. Addison-Wesley.
 * Bartlett, M. S. (1978). An Introduction to Stochastic Processes, with Special Reference to Methods and Applications. Cambridge University Press.
 * Doob, J. L. (1953).Stochastic Processes. Wiley.

Scholarly Articles

 * Geering, H. P., Dondi, G., Herzog, F., & Keel, S. (2011). Stochastic systems. Course script. (link)

Software

 * StochPy - Python
 * Bridge.jl - Julia
 * Brownian.jl - Julia
 * RandLib - C++
 * binary-martingale - Python

Other Resources

 * Stochastic Processes - Notebook
 * Random Fields - Notebook
 * Time Series - Notebook