摘要: We investigate the behaviour of P(R ≥ r) and ≤ - as r → ∞ for random variable R:= Formula math M k , where ((Q )) ∈ N is an independent, identically distributed sequence with P(-1 1) = 1. Random variables this type appear in insurance mathematics, solutions stochastic difference equations, analysis probabilistic algorithms elsewhere. Exponential Poissonian tail can arise.
jstor.org
sci-hub.se 参考文章(18)
Hikaru Ohkubo, ON THE ASYMPTOTIC TAIL BEHAVIORS OF INFINITELY DIVISIBLE DISTRIBUTIONS The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学. ,vol. 27, pp. 77- 89 ,(1979)
Paul Embrechts, Charles Goldie, Perpetuities and Random Equations Asymptotic Statistics. pp. 75- 86 ,(1994) , 10.1007/978-3-642-57984-4_6
Edward C. Waymire, Rabi N. Bhattacharya, Stochastic processes with applications ,(1990)
Jean-Fran�ois Chamayou, G�rard Letac, Explicit stationary distributions for compositions of random functions and products of random matrices Journal of Theoretical Probability. ,vol. 4, pp. 3- 36 ,(1991) , 10.1007/BF01046992
Hans Arnfinn Karlsen, Existence of moments in a stationary stochastic difference equation Advances in Applied Probability. ,vol. 22, pp. 129- 146 ,(1990) , 10.2307/1427601
Mark Brown, Error bounds for exponential approximations of geometric convolutions Annals of Probability. ,vol. 18, pp. 1388- 1402 ,(1990) , 10.1214/AOP/1176990750
Charles M. Goldie, IMPLICIT RENEWAL THEORY AND TAILS OF SOLUTIONS OF RANDOM EQUATIONS Annals of Applied Probability. ,vol. 1, pp. 126- 166 ,(1991) , 10.1214/AOAP/1177005985
Lennart Bondesson, A General Result on Infinite Divisibility Annals of Probability. ,vol. 7, pp. 965- 979 ,(1979) , 10.1214/AOP/1176994890
A. K. Grincevićius, One limit distribution for a random walk on the line Lithuanian Mathematical Journal. ,vol. 15, pp. 580- 589 ,(1975) , 10.1007/BF00969789
Olof Thorin, On the infinite divisibility of the lognormal distribution Scandinavian Actuarial Journal. ,vol. 1977, pp. 121- 148 ,(1977) , 10.1080/03461238.1977.10405635