The potential kernel and hitting probabilities for the general stable process in $R^{N}$
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- by W. E. Pruitt and S. J. Taylor
- Trans. Amer. Math. Soc. 146 (1969), 299-321
- DOI: https://doi.org/10.1090/S0002-9947-1969-0250372-3
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References
- R. M. Blumenthal and R. K. Getoor, Some theorems on stable processes, Trans. Amer. Math. Soc. 95 (1960), 263–273. MR 119247, DOI 10.1090/S0002-9947-1960-0119247-6 A. Erdélyi et al., Higher transcendental functions, Vol. II, Bateman Manuscript Project, McGraw-Hill, New York, 1953. G. A. Hunt, Markov processes and potentials. I, II, III, Illinois J. Math. 1 (1957), 44-93, 316-369; 2 (1958), 151-213.
- Naresh Jain and William E. Pruitt, The correct measure function for the graph of a transient stable process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 (1968), 131–138. MR 228064, DOI 10.1007/BF01851003 P. Lévy, Théorie de l’addition des variables aléatoires, Gauthier-Villars, Paris, 1937.
- Steven Orey, Polar sets for processes with stationary independent increments, Markov Processes and Potential Theory (Proc. Sympos. Math. Res. Center, Madison, Wis., 1967) Wiley, New York, 1967, pp. 117–126. MR 0229305 G. Polya, On the zeroes of an integral function represented by Fourier’s integral, Messenger of Math. 52 (1923), 185-188.
- Sidney C. Port, A remark on hitting places for transient stable process, Ann. Math. Statist. 39 (1968), 365–371. MR 225386, DOI 10.1214/aoms/1177698397
- S. C. Port and C. J. Stone, The asymmetric Cauchy processes on the line, Ann. Math. Statist. 40 (1969), 137–143. MR 235619, DOI 10.1214/aoms/1177697810
- 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 258126, DOI 10.1007/BF00538749
- A. V. Skorohod, Asymptotic formulas for stable distribution laws, Select. Transl. Math. Statist. and Probability, Vol. 1, Inst. Math. Statist. and Amer. Math. Soc., Providence, R.I., 1961, pp. 157–161. MR 0116373
- S. J. Taylor, Sample path properties of a transient stable process, J. Math. Mech. 16 (1967), 1229–1246. MR 0208684
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- 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