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Original Articles

Asymptotic behavior of some hitting probabilities for sums of IID Gaussian random sets

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Pages 4318-4332 | Received 01 Jul 2015, Accepted 02 Nov 2015, Published online: 18 Jan 2017

References

  • Asmussen, S. (2003). Applied Probability and Queues. 2nd ed. New York: Springer-Verlag.
  • Asmussen, S., Glynn, P. W. (2007). Stochastic Simulation: Algorithms and Analysis. New York: Springer.
  • Beneš, V., Rataj, J. (2004). Stochastic Geometry: Selected Topics. Boston, MA: Kluwer Academic Publishers.
  • Cerf, R. (1999). Large deviations for sums of iid random compact sets. Proceedings of the American Mathematical Society 127(8):2431–2436.
  • Collamore, J. F. (1996). Hitting probabilities and large deviations. Annals of Probability 24(4):2065–2078.
  • Collamore, J. F. (2002). Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors. Annals of Applied Probability 12(1):382–421.
  • Dembo, A., Zeitouni, O. (1998). Large Deviations Techniques and Applications. 2nd ed. New York: Springer-Verlag.
  • Dieker, A. B., Mandjes, M. (2005). On asymptotically efficient simulation of large deviation probabilities. Advances in Applied Probability 37(2):539–552.
  • Gatto, R. (2014). Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes. Applied Mathematics and Computation 243:91–104.
  • Lehtonen, T., Nyrhinen, H. (1992a). Simulating level crossing probabilities by importance sampling. Advances in Applied Probability 24(4):858–874.
  • Lehtonen, T., Nyrhinen, H. (1992b). On asymptotically efficient simulation of ruin probabilities in a Markovian environment. Scandinavian Actuarial Journal 1992(1):60–75.
  • Mathai, A. M., Provost, S. B. (1992). Quadratic Forms in Random Variables. Theory and Applications. New York: Marcel Dekker, Inc.
  • Matheron, G. (1975). Random Sets and Integral Geometry. New York: John Wiley & Sons.
  • Miao, Y. (2009). Moderate deviation principles for sums of iid random compact sets. Commentationes Mathematicae Universitatis Carolinae 50(1):103–111.
  • Molchanov, I. (2005). Theory of Random Sets. London: Springer-Verlag.
  • Sadowsky, J. S. (1996). On Monte Carlo estimation of large deviations probabilities. Annals of Applied Probability 6(2):399–422.
  • Siegmund, D. (1976). Importance sampling in the Monte Carlo study of sequential test. Annals of Statistics 4(4):673–684.
  • Stoyan, D., Kendall, W. S., Mecke, J. (1987). Stochastic Geometry and its Applications. With a Foreword by D.G. Kendall. Chichester: John Wiley & Sons.

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