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Copulæ of Processes Related to the Brownian Motion: A Brief Survey

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 336))

Abstract

The copulas of a few stochastic processes related to the Brownian motion are derived; specifically, if \((X_t)\) is one such process, the copula of the pair \((X_s,X_t)\) is determined for \(s<t\).

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References

  1. Darsow, W.F., Nguyen, B.E., Olsen, T.: Copulas and Markov processes. Illinois J. Math. 36, 600–642 (1992)

    MathSciNet  MATH  Google Scholar 

  2. Durante, F., Sempi, C.: Principles of Copula Theory. Chapman & Hall/CRC, Boca Raton (2015)

    Book  Google Scholar 

  3. Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus, 2nd edn. Springer, Berlin (1991)

    MATH  Google Scholar 

  4. Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)

    MATH  Google Scholar 

  5. Rogers, L.C.G., Williams, D.: Diffusions, Markov processes and martingales. In: Foundations, 2nd Edn. Cambridge University Press (2000)

    Google Scholar 

  6. Schmitz, V.: Copulas and stochastic processes. Ph.D. Dissertation, Rheinische-Westfälische Technische Hochschule, Aachen, Germany (2003)

    Google Scholar 

  7. Sklar, A.: Fonctions de répartition à \(n\) dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)

    MathSciNet  Google Scholar 

  8. Stirzaker, D.: Stochastic processes and models. Oxford University Press (2005)

    Google Scholar 

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Correspondence to Carlo Sempi .

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Sempi, C. (2016). Copulæ of Processes Related to the Brownian Motion: A Brief Survey. In: Saminger-Platz, S., Mesiar, R. (eds) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-319-28808-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-28808-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28807-9

  • Online ISBN: 978-3-319-28808-6

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