IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v58y1995i1p121-137.html
   My bibliography  Save this article

On the typical level crossing time and path

Author

Listed:
  • Nyrhinen, Harri

Abstract

Let Y1, Y2, ... be a stochastic process and M a positive real number. Define the level crossing time TM = inf{n|Yn > M} (TM) = + [infinity] if Yn

Suggested Citation

  • Nyrhinen, Harri, 1995. "On the typical level crossing time and path," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 121-137, July.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:1:p:121-137
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)00079-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gerber, Hans U., 1982. "Ruin theory in the linear model," Insurance: Mathematics and Economics, Elsevier, vol. 1(3), pages 213-217, July.
    2. Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nyrhinen, Harri, 2001. "Finite and infinite time ruin probabilities in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 265-285, April.
    2. Ghosh, Souvik & Samorodnitsky, Gennady, 2010. "Long strange segments, ruin probabilities and the effect of memory on moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2302-2330, December.
    3. Barbe, Ph. & McCormick, W.P., 2010. "An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 801-828, June.
    4. Harri Nyrhinen, 2015. "On real growth and run-off companies in insurance ruin theory," Papers 1511.01763, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Barbe, Ph. & McCormick, W.P., 2010. "An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 801-828, June.
    2. Albrecher Hansjörg & Kantor Josef, 2002. "Simulation of ruin probabilities for risk processes of Markovian type," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 111-128, December.
    3. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2016. "Solvency capital requirement for a temporal dependent losses in insurance," Economic Modelling, Elsevier, vol. 58(C), pages 588-598.
    4. Wenzhi Yang & Shuhe Hu & Xuejun Wang, 2012. "Complete Convergence for Moving Average Process of Martingale Differences," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-16, July.
    5. Yun-xia, Li & Li-xin, Zhang, 2004. "Complete moment convergence of moving-average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 191-197, December.
    6. Yun-Xia, Li, 2006. "Precise asymptotics in complete moment convergence of moving-average processes," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1305-1315, July.
    7. Muller, Alfred & Pflug, Georg, 2001. "Asymptotic ruin probabilities for risk processes with dependent increments," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 381-392, June.
    8. Jong-Il Baek & Sung-Tae Park, 2010. "RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications," Journal of Theoretical Probability, Springer, vol. 23(2), pages 362-377, June.
    9. Zhang, Zhiqiang & Yuen, Kam C. & Li, Wai Keung, 2007. "A time-series risk model with constant interest for dependent classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 32-40, July.
    10. Ahmed, S. Ejaz & Antonini, Rita Giuliano & Volodin, Andrei, 2002. "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 185-194, June.
    11. Zhang, Li-Xin, 1996. "Complete convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 165-170, October.
    12. Zhou, Xingcai, 2010. "Complete moment convergence of moving average processes under [phi]-mixing assumptions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 285-292, March.
    13. Christ, Ralf & Steinebach, Josef, 1995. "Estimating the adjustment coefficient in an ARMA(p, q) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 149-161, October.
    14. Ramsés H. Mena & Luis E. Nieto-Barajas, 2007. "Exchangeable Claims Sizes in a Compound Poisson Type Proces," ICER Working Papers - Applied Mathematics Series 19-2007, ICER - International Centre for Economic Research.
    15. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "Complete moment convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 839-846, May.
    16. Chen, Pingyan & Hu, Tien-Chung & Volodin, Andrei, 2009. "Limiting behaviour of moving average processes under [phi]-mixing assumption," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 105-111, January.
    17. Lovas, Attila & Rásonyi, Miklós, 2021. "Markov chains in random environment with applications in queuing theory and machine learning," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 294-326.
    18. Jiang, Tiefeng & Rao, M. Bhaskara & Wang, Xiangchen, 1995. "Large deviations for moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 309-320, October.
    19. Federico Camerlenghi & Claudio Macci & Elena Villa, 2021. "Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1011-1035, October.
    20. Hélène Cossette & Etienne Marceau & Véronique Maume-Deschamps, 2011. "Adjustment Coefficient for Risk Processes in Some Dependent Contexts," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 695-721, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:58:y:1995:i:1:p:121-137. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.