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On the Dependence Structure of Certain Multi-dimensional Ito Processes and Corresponding Hitting Times

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  • Ebrahimi, Nader

Abstract

A direct approach to derive dependence properties among components of multi-dimensional stochastic processes has been discussed by N. Ebrahimi (1994, J. Multivariate Anal.50, 55-67). Dependence properties among hitting times involving multi-dimensional stochastic processes has been initiated by N. Ebrahimi (1987, J. Appl. Probab.24, 115-122) and explored further by N. Ebrahimi and T. Ramalingham (1988, J. Appl. Probab.25, 355-362; 1989, J. Appl. Probab.26, 287-295). Let X(t)=(X1(t), ..., Xk(t)) be an Ito process assuming values in Rk. In this article, under certain conditions, we show that the process X(t) has a certain dependence structure. We also consider the first passage problem involving X(t) and discuss the dependence structure among hitting times of X1(t), ..., and Xk(t).

Suggested Citation

  • Ebrahimi, Nader, 2002. "On the Dependence Structure of Certain Multi-dimensional Ito Processes and Corresponding Hitting Times," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 128-137, April.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:128-137
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    References listed on IDEAS

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    1. Ebrahimi, N., 1994. "On the Dependence of Structure of Multivariate Processes and Corresponding Hitting Times," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 55-67, July.
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    Cited by:

    1. Nicole Bäuerle & Anja Blatter & Alfred Müller, 2008. "Dependence properties and comparison results for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 161-186, February.
    2. Dan Zhu & Ming Zhou & Chuancun Yin, 2023. "Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    3. Bäuerle Nicole & Schmock Uwe, 2012. "Dependence properties of dynamic credit risk models," Statistics & Risk Modeling, De Gruyter, vol. 29(3), pages 243-268, August.

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