Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

A Sharp Result of Random Upper Functions for Levy Processes

  • Kim, Gwan-Young (Department of Statistics, Kangwon Natioal University, Chuncheon 200-701) ;
  • Joo, Sang-Yeol (Department of Statistics, Kangwon Natioal University, Chuncheon 200-701) ;
  • Kim, Yun-Kyong (Department of Mathematics, Dongshin University, Naju 520-714)
  • Published : 1995.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we show that the result of random upper functions for Levy processes obtained by Joo(1993) can be sharpened under some additional assumption. This is the continuous analogue of result obtained by Griffin and Kuelbs (1989) for sums of i.i.d. random varialbles.

Keywords

References

  1. Bulletin of the London Mathematical Society v.18 Variants on the law of the iterated logarithm Bingham,N.H.
  2. Journal of Mathematics and Mechanics v.10 Sample functions of stochastic processes with stationary independent increments Blumenthal,R.M.;Getoor,R.K.
  3. Indiana University Mathematics Journal v.21 Upper functions for symmetric processes with stationary independent increments Fristedt,B.E.
  4. The Theory of Stochastic Processes Ⅱ Gihman,I.I.;Skorokhod,A.V.
  5. Annals of Probability v.17 Self-normalized laws of the iterated logarithm Griffin,Ph.S.;Kuelbs,J.D.
  6. Journal of the Korean Statistical Society v.22 Random upper functions for Levy processes Joo,S.Y.
  7. Stochastic Analysis and Applications v.9 Upper functions for Levy processes having only negative jumps Kim,Y.K.;Wee,I.S.
  8. Annals of Probability v.9 General one-sided laws of the iterated logarithm Pruitt,W.E.
  9. Probability Theory and Related Fields v.77 Lower functions for processes with wtationary independent increments Wee,I.S.