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On a continuous analogue of the stochastic difference equation Xn=[rho]Xn-1+Bn

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  • Wolfe, Stephen James

Abstract

Let B1, B2, ... be a sequence of independent, identically distributed random variables, letX0 be a random variable that is independent ofBn forn[greater-or-equal, slanted]1, let [rho] be a constant such that 0 +[infinity] if and only ifE[log+|B(1)|]

Suggested Citation

  • Wolfe, Stephen James, 1982. "On a continuous analogue of the stochastic difference equation Xn=[rho]Xn-1+Bn," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 301-312, May.
    • Handle: RePEc:eee:spapps:v:12:y:1982:i:3:p:301-312
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    Cited by:

    1. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    2. Hinderks, W.J. & Wagner, A., 2020. "Factor models in the German electricity market: Stylized facts, seasonality, and calibration," Energy Economics, Elsevier, vol. 85(C).
    3. Jurek, Zbigniew J., 2014. "Remarks on the factorization property of some random integrals," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 192-195.
    4. Borovkov, Konstantin & Novikov, Alexander, 2008. "On exit times of Lévy-driven Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1517-1525, September.
    5. Maejima, Makoto & Ueda, Yohei, 2010. "[alpha]-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2363-2389, December.
    6. Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2019. "Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5113-5150.
    7. Wang, Xiaolong & Feng, Jing & Liu, Qi & Li, Yongge & Xu, Yong, 2022. "Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    8. Zheng, Jing & Lin, Zhengyan & Tong, Changqing, 2009. "The Hausdorff dimension of the range for the Markov processes of Ornstein–Uhlenbeck type," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2008-2013.
    9. Brockwell, Peter J. & Lindner, Alexander, 2015. "Prediction of Lévy-driven CARMA processes," Journal of Econometrics, Elsevier, vol. 189(2), pages 263-271.
    10. Bhatti, T. & Kern, P., 2017. "An integral representation of dilatively stable processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 209-227.

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