| Some results of precise asymptotics for Levy processes | 
| Dan Chen, Su Chun | 
| 2004, выпуск 2, С. 205–210 | 
| Аннотация | 
| 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 $\{X(t), t \le 0 \}$. | 
| Ключевые слова: precise asymptotic, Levy process, stable process, Fuk-Nagaev type inequality | 
| Полный текст статьи (файл PDF) | 
| Библиографический список | 
| [1] A. Gut, A. Spataru, “Precise asymptotics in the law of the iterated logarithm”, Ann. Probab., 28 (2000), 1870–1883. [2] A. Gut, A. Spataru, “Precise asymptotics in the Baum – Katz and Davis laws of large numbers”, J. Math. Anal. Appl., 248 (2000), 233–246. [3] C. C. Heyde, “A supplement to the strong law of large numbers”, J. Appl. Probab., 12 (1975), 173–175. [4] D. H. Fuk, S. V. Nagaev, “Probability inequalities for sums of independent random variables”, Theory Probab. Appl., 16 (1971), 643–660. [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), 328–333. [8] Z. Hu, C. Su, “A supplement to a Theorem of Gut and Spataru”, J. Math. Anal. Appl., 289:2 (2004), 522–529. |