Summary
Consider a completely asymmetric stable process with characteristic exponent less than one. J. Hawkes (1971, Z. Wahrscheinlichkeitstheor. Verw. Geb.17, 23–32) proved a result for the lower Lipschitz condition. In the present paper a functional form for this result is proved.
References
Chung, K.L., P. Erdös & T. Sirao: On the Lipschitz's condition for Brownian motion. J. Math. Soc. Japan11, 263–274 (1959)
Freedman, D.: Brownian motion and diffusion. San Francisco: Holden-Day 1971
Hawkes, J.: A lower Lipschitz condition for the stable subordinator. Z. Wahrscheinlichkeitstheor. Verw. Geb.17, 23–32 (1971)
Lévy, P.: Processus stochastiques et mouvement Brownien, Paris: Gauthier-Villars 1948
Mijnheer, J.L.: Properties of the sample functions of the completely asymmetric stable process. Z. Wahrscheinlichkeitstheor. Verw. Geb.27, 153–170 (1973)
Mijnheer, J.L.: Sample path properties of stable processes. Amsterdam: Math. Centre 1975
Mueller, C.: A unification of Strassen's law and Lévy's modulus of continuity. Z. Wahrscheinlichkeitstheor. Verw. Geb.56, 163–179 (1981)
Strassen, V.: An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.3, 211–226 (1964)
Wichura, M.: Functional laws of the iterated logarithm for the partial sums of i.i.d. random variables in the domain of attraction of a completely asymmetric stable law. Ann. Probab.2, 1108–1138 (1974)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mijnheer, J. A functional form for the lower Lipschitz condition for the stable subordinator. Probab. Th. Rel. Fields 77, 515–520 (1988). https://doi.org/10.1007/BF00959614
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00959614
Keywords
- Stochastic Process
- Probability Theory
- Functional Form
- Mathematical Biology
- Stable Process