Some results of precise asymptotics for Levy processes

Dan Chen, Su Chun

2004, 2, . 205210

Let $\{X(t), t \le 0 \}$ be a Levy processes with $EX(1)=0$ and $EX2(1)<\infty$. In this paper, we give two precise asymptotic theorems for $\{X(t), t \le 0 \}$.

precise asymptotic, Levy process, stable process, Fuk-Nagaev type inequality

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[1] A. Gut, A. Spataru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab., 28 (2000), 18701883.
[2] A. Gut, A. Spataru, Precise asymptotics in the Baum Katz and Davis laws of large numbers, J. Math. Anal. Appl., 248 (2000), 233246.
[3] C. C. Heyde, A supplement to the strong law of large numbers, J. Appl. Probab., 12 (1975), 173175.
[4] D. H. Fuk, S. V. Nagaev, Probability inequalities for sums of independent random variables, Theory Probab. Appl., 16 (1971), 643660.
[5] J. Bertoin, Levy Processes, Cambridge University Press, Cambridge, 1996.
[6] K. Sato, Levy Processes and Infinitely Divisible Distribution, Cambridge University Press, Cambridge, 1999.
[7] R. Chen, A remark on the tail probability of a distribution, J. Multivariate Anal., 1978 (1978), 328333.
[8] Z. Hu, C. Su, A supplement to a Theorem of Gut and Spataru, J. Math. Anal. Appl., 289:2 (2004), 522529.