Summary
Let ((X(t)), P x) be an α-self-similar isotropic Markov process on R d {0}. A representation of (X(t)), in terms of the radial and angular process which generalizes the skew product representation for Brownian motion is given.
References
Bingham, N.H.: Random walk on spheres. Z. Wahrsheinlichkeitstheorie. verw. Geb. 22, 169–192 (1972)
Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York: Academic Press 1968
Bochner, S.: Positive zonal functions on spheres, Proc. Natl. Acad. Sci. (USA) 40, 1141–1147, (1954)
Bochner, S.: Harmonic analysis and the theory of probability. Univ. Calif. Press 1955
Galmarino, A.R.: Representation of an isotropic diffusion as a skew product. Z. Wahrscheinlichkeitstheor. verw. Geb. 1, 359–378 (1963)
Gangolli, R.: Isotropic infinitely-divisible measures on symmetric spaces. Acta Math. 111, 213–246 (1964)
Itô, K., McKean, H.P.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965
Kiu, S.W.: Semi-stable Markov processes in R n. Stochastic Processes Appl. 10, 183–191 (1980)
Lamperti, J.W.: Semi-stable Markov processes I. Z. Wahrscheinlichkeitstheor. verw. Geb. 22, 205–225 (1972)
Lamperti, J.W.: Semi-stable stochastic processes. Trans. Am. Math. Soc. 104, 62–78 (1962)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Graversen, S.E., Vuolle-Apiala, J. α-self-similar Markov processes. Probab. Th. Rel. Fields 71, 149–158 (1986). https://doi.org/10.1007/BF00366277
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00366277
Keywords
- Stochastic Process
- Brownian Motion
- Probability Theory
- Markov Process
- Mathematical Biology