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Convergence of large deviation rates based on a link between wave governed random motions and ruin processes

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  • Macci, Claudio

Abstract

It is possible to consider a sequence of wave governed random motions such that their paths converge to the path of a suitable ruin process with exponentially distributed claim sizes (see the proof of Theorem 1 in [Mazza, C., Rulliére, D., 2004. A link between wave governed random motions and ruin processes. Insurance Math. Econom. 35, 205-222]). In this paper we verify that some large deviation rates for these wave governed random motions converge to the analogous rates for the same ruin process.

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  • Macci, Claudio, 2009. "Convergence of large deviation rates based on a link between wave governed random motions and ruin processes," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 255-263, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:2:p:255-263
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    References listed on IDEAS

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    1. Paolo Baldi & Mauro Piccioni, 1999. "Importance Sampling for Continuous Time Markov Chains and Applications to Fluid Models," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 375-390, December.
    2. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
    3. Baldi, Paolo & Piccioni, Mauro, 1999. "A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 107-115, January.
    4. Claudio Macci, 2008. "Inequalities between some large deviation rates," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(1), pages 83-92, January.
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    Cited by:

    1. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
    2. Macci, Claudio, 2016. "Large deviations for some non-standard telegraph processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 119-127.

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