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Embedding a stochastic difference equation into a continuous-time process

Author

Listed:
  • de Haan, L.
  • Karandikar, R. L.

Abstract

A concept of divisibility is introduced for stochastic difference equations. Infinite divisibility then leads to a continuous time process in which a nested sequence of divisible stochastic difference equations can be embedded.

Suggested Citation

  • de Haan, L. & Karandikar, R. L., 1989. "Embedding a stochastic difference equation into a continuous-time process," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 225-235, August.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:2:p:225-235
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    Cited by:

    1. Behme, Anita & Lindner, Alexander & Reker, Jana & Rivero, Victor, 2021. "Continuity properties and the support of killed exponential functionals," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 115-146.
    2. Lindner, Alexander & Maller, Ross, 2005. "Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1701-1722, October.
    3. Behme, Anita & Lindner, Alexander, 2012. "Multivariate generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1487-1518.
    4. Dong, Y. & Spielmann, J., 2020. "Weak limits of random coefficient autoregressive processes and their application in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 1-11.
    5. Kevei, Péter, 2018. "Ergodic properties of generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 156-181.
    6. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660.
    7. Chou, Ching-Sung & Lin, Hsien-Jen, 2007. "Pricing model for zero coupon bonds driven by Bessel-squared interest processes with a jump," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 475-482, March.

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