\[\renewcommand{\var}{\operatorname{Var}} \renewcommand{\corr}{\operatorname{Corr}} \renewcommand{\dd}{\mathrm{d}} \renewcommand{\bb}[1]{\mathbb{#1}} \renewcommand{\vv}[1]{\boldsymbol{#1}} \renewcommand{\rv}[1]{\mathsf{#1}} \renewcommand{\vrv}[1]{\vv{\rv{#1}}} \renewcommand{\disteq}{\stackrel{d}{=}} \renewcommand{\gvn}{\mid} \renewcommand{\Ex}{\mathbb{E}} \renewcommand{\Pr}{\mathbb{P}}\]

Some useful generalisations of autoregressive (i.e. AR(1), Ornstein-Uhlenbeck) processes.

## References

Barndorff-Nielsen, O. E. 2001. “Superposition of Ornstein–Uhlenbeck Type Processes.”

*Theory of Probability & Its Applications*45 (2): 175–94.
Barndorff-Nielsen, Ole Eiler, and Robert Stelzer. 2011. “Multivariate supOU Processes.”

*The Annals of Applied Probability*21 (1): 140–82.
Barndorff-Nielsen, Ole E., and Neil Shephard. 2001. “Non-Gaussian Ornstein–Uhlenbeck-Based Models and Some of Their Uses in Financial Economics.”

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*63 (2): 167–241.
Foti, Nicholas J., and Sinead Williamson. 2012. “A Survey of Non-Exchangeable Priors for Bayesian Nonparametric Models.”

*arXiv:1211.4798 [Cs, Stat]*, November.
Grifﬁn, J E. n.d. “Time-Dependent Stick-Breaking Processes,” 34.

Griffin, J.E. 2011. “The Ornstein–Uhlenbeck Dirichlet Process and Other Time-Varying Processes for Bayesian Nonparametric Inference.”

*Journal of Statistical Planning and Inference*141 (11): 3648–64.
Grunwald, G K, R J Hyndman, and L M Tedesco. n.d. “A Uniﬁed View of Linear AR(1) Models,” 26.

Pigorsch, Christian, and Robert Stelzer. 2009. “On the Definition, Stationary Distribution and Second Order Structure of Positive Semidefinite Ornstein–Uhlenbeck Type Processes.”

*Bernoulli*15 (3): 754–73.
Wolpert, Robert L. 2021. “Lecture Notes on Stationary Gamma Processes.”

*arXiv:2106.00087 [Math]*, May.
Wolpert, Robert L., and Lawrence D. Brown. 2021. “Markov Infinitely-Divisible Stationary Time-Reversible Integer-Valued Processes.”

*arXiv:2105.14591 [Math]*, May.
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