Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The potential kernel and hitting probabilities for the general stable process in $ R\sp{N}$


Authors: W. E. Pruitt and S. J. Taylor
Journal: Trans. Amer. Math. Soc. 146 (1969), 299-321
MSC: Primary 60.60
DOI: https://doi.org/10.1090/S0002-9947-1969-0250372-3
MathSciNet review: 0250372
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] R. M. Blumenthal and R. K. Getoor, Some theorems on stable processes, Trans. Amer. Math. Soc. 95 (1960), 263-273. MR 0119247 (22:10013)
  • [2] A. Erdélyi et al., Higher transcendental functions, Vol. II, Bateman Manuscript Project, McGraw-Hill, New York, 1953.
  • [3] G. A. Hunt, Markov processes and potentials. I, II, III, Illinois J. Math. 1 (1957), 44-93, 316-369; 2 (1958), 151-213.
  • [4] N. Jain and W. E. Pruitt, The correct measure function for the graph of a transient stable process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 (1968), 131-138. MR 0228064 (37:3648)
  • [5] P. Lévy, Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris, 1937.
  • [6] S. Orey, ``Polar sets for processes with stationary independent increments'' in Markov processes and potential theory, edited by J. Chover, Wiley, New York, 1967, pp. 117-126. MR 0229305 (37:4879)
  • [7] G. Polya, On the zeroes of an integral function represented by Fourier's integral, Messenger of Math. 52 (1923), 185-188.
  • [8] S. C. Port, A remark on hitting places for transient stable process, Ann. Math. Statist. 39 (1968), 365-371. MR 0225386 (37:980)
  • [9] S. C. Port and C. J. Stone, The asymmetric Cauchy processes on the line, Ann. Math. Statist. 40 (1969), 137-143. MR 0235619 (38:3922)
  • [10] W. E. Pruitt and S. J. Taylor, Sample path properties of processes with stable components, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 12 (1969), 267-289. MR 0258126 (41:2773)
  • [11] A. V. Skorohod, Asymptotic formulas for stable distribution laws, Dokl. Akad. Nauk SSSR 98 (1954), 731-734; English transl., Selected Transls. in Math. Stat. and Prob. 1 (1961), 157-161. MR 0116373 (22:7161)
  • [12] S. J. Taylor, Sample path properties of a transient stable process, J. Math. Mech. 16 (1967), 1229-1246. MR 0208684 (34:8493)
  • [13] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Univ. Press, Cambridge, 1944. MR 0010746 (6:64a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60.60

Retrieve articles in all journals with MSC: 60.60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0250372-3
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society