Stochastic Process

From Ioannis Kourouklides
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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[edit]

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)
  • 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

Online Courses[edit]

Video Lectures[edit]

Lecture Notes[edit]

Books and Book Chapters[edit]

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[edit]

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


See also[edit]

Other Resources[edit]