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
- Weak-sense Stationary Process / Wide-sense Stationary Process
- Strictly Stationary Process / Strongly Stationary Process
- Ergodicity / Ergodic Process
- 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)
- 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 Random Field / Markov Network
- 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
- 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
- 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
- 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.
- Geering, H. P., Dondi, G., Herzog, F., & Keel, S. (2011). Stochastic systems. Course script. (link)
- State Space Models / Linear Dynamical Systems
- Kalman filter
- Information Theory
- Probability Theory
- Estimation Theory / System Identification / Statistical Signal Processing
- Bayesian Nonparametrics
- Monte Carlo Methods / Stochastic Simulation
- Computational Finance
- Artificial Neural Networks