Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

ON SELFSIMILAR AND SEMI-SELFSIMILAR PROCESSES WITH INDEPENDENT INCREMENTS

  • Published : 1998.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

Keywords

References

  1. Lectures from Markov processes to Brownian motion K.L. Chung
  2. Pacific J. Math. v.21 Sample function behavior of increasing processes with stationary, independent increments B.E. Fristedt
  3. A. Wahrsch. Verw. Gebiete v.18 Lower functions for increasing random walks and subordinators B.E. Fristedt;W.E. Pruitt
  4. Lecture Notes in Mathematics(springer) v.784 Transience and recyrrence of Markov processes R.K. Getoor
  5. Limit distructions for sums of independent random variables(2nd ed.) B.V. Gnedenko;A.N. Kolmogorov
  6. Theorie de l'addition des variables aleatoires($2^e$ ed.) P. Levy
  7. Kodai Math. J. v.13 Recurrence and transience of Gaussian difffusion processes J.J. Liou
  8. Semi-selfdecomposable distributions and a new class of limit theorems M. Maejima;Y. Naito
  9. Semi-selfsimilar processes M. Maejima;K. Sato
  10. Remarks on semi-seldsimilar processes M. Maejima;K. Sato;T. Watamabe
  11. J. Multivar. Anal. v.10 Class L of multivariate distribution and its subclasses K. Sato
  12. Kahou katei(additive processes) K. Sato
  13. Distributions of class L and self-similar processes with independent increments K. Sato;T. Hida(et al.)(ed.)
  14. Prob. Th. Rel. Fields v.89 Self-similar processes with independent increments K. Sato
  15. Time evolution of Levy processes K. Sato;N. Kono(ed.);N.R. Shieh(ed.)
  16. Proc. Amer. Math. Soc. v.49 The supports of infinitely divisible distribution functions H.G. Tucker
  17. Prob. Th. Rel. Fields v.104 Sample function behavior of increasing processes of class L T. Watanabe
  18. Transience conditions for self-similar additive processes K. Yamamuro