Journal of the Korean Statistical Society

  • 제22권1호
  • /
  • Pages.93-111
  • /
  • 1993
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Random Upper Functions for Levy Processes

  • Joo, Sang-Yeol (Department of Statistics, Kangweon National University, Chuncheon, 200-701)
  • 발행 : 1993.06.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let ${X(t) : t \geq 0}$ be a real-valued stochastics process with stationary independent increments. In this paper, under the condition of stochastic compactness, we obtain appropriate function $\alpha(t)$ and random function $\beta(t)$ such that for some positive finite constant C, lim sup${X(t) - \alpha(t)}/\beta(t) = C$ a.s. both as t tends to zero and infinity.

키워드

참고문헌

  1. Journal of the Korean Mathematical Society v.22 The class of limit Laws for Levy processes Ahn,W.C.;Wee,I.S.
  2. Bulletin of the London Mathematical Society v.18 Variants on the law of the iterated logarithm Bingham,N.H.
  3. Journal of Mathematical Mechanics v.10 Sample functions of stochastic processes with stationary independent increments Blumenthal,R.M.;Getoor,R.K.
  4. Journal of Mathematical Mechanics v.18 An extension of the law of the iterated logarithm to variables without variance Feller,W.
  5. Advances in Probability and Related Topics v.3 Sample functions of stochastic processes with stationary independent increments Fristedt,B.E.
  6. The theory of stochastic processes Ⅱ Gihman,I.I.;Skorokhod,A.V.
  7. Zeitschrift f$\"{u}$r Wahrscheinlichkeitstheorie und verwandte Gebiete v.68 Laws of the iterated logarithm for symmetric stable processes Griffin,Ph.S.
  8. Annals of Probability v.17 Self-normalized laws of the iterated logarithm Griffin,Ph.S.;Kuelbs,J.D.
  9. Journal of the Korean Statistical Society v.17 General laws of the iterated logarithm for Levy processes Kim,Y.K.;Wee,I.S.
  10. Stochastic Analysis and Applications v.9 Upper functions for Levy processes having only negative jumps Kim,Y.K.;Wee,I.S.
  11. Annals of Probability v.9 General one-sided laws of the iterated logarithm Pruitt,W.E.
  12. Probability Theory and Related Fields v.77 Lower functions for processes with stationary independent increments Wee,I.S.