Stochastic Process

From Ioannis Kourouklides
Jump to navigation Jump to search

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)

Software[edit]

See also[edit]

Other Resources[edit]