First passage times for symmetric stable processes in space

Author:
R. K. Getoor

Journal:
Trans. Amer. Math. Soc. **101** (1961), 75-90

MSC:
Primary 60.60

DOI:
https://doi.org/10.1090/S0002-9947-1961-0137148-5

MathSciNet review:
0137148

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References | Similar Articles | Additional Information

- R. M. Blumenthal and R. K. Getoor,
*Some theorems on stable processes*, Trans. Amer. Math. Soc.**95**(1960), 263–273. MR**119247**, DOI https://doi.org/10.1090/S0002-9947-1960-0119247-6 - R. M. Blumenthal and R. K. Getoor,
*The asymptotic distribution of the eigenvalues for a class of Markov operators*, Pacific J. Math.**9**(1959), 399–408. MR**107298** - S. Bochner and K. Chandrasekharan,
*Fourier Transforms*, Annals of Mathematics Studies, No. 19, Princeton University Press, Princeton, N. J.; Oxford University Press, London, 1949. MR**0031582** - Joanne Elliott,
*Absorbing barrier processes connected with the symmetric stable densities*, Illinois J. Math.**3**(1959), 200–216. MR**102754** - A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi,
*Tables of integral transforms. Vol. II*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR**0065685** - R. K. Getoor,
*Additive functionals of a Markov process*, Pacific J. Math.**7**(1957), 1577–1591. MR**94850** - R. K. Getoor,
*Markov operators and their associated semi-groups*, Pacific J. Math.**9**(1959), 449–472. MR**107297** - Einar Hille and Ralph S. Phillips,
*Functional analysis and semi-groups*, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR**0089373** - M. Kac,
*Some remarks on stable processes with independent increments*, Probability and statistics: The Harald Cramér volume (edited by Ulf Grenander), Almqvist & Wiksell, Stockholm; John Wiley & Sons, New York, 1959, pp. 130–138. MR**0107898** - Mark Kac and Harry Pollard,
*The distribution of the maximum of partial sums of independent random variables*, Canad. J. Math.**2**(1950), 375–384. MR**36465**, DOI https://doi.org/10.4153/cjm-1950-034-9 - Wilhelm Magnus and Fritz Oberhettinger,
*Formulas and Theorems for the Special Functions of Mathematical Physics*, Chelsea Publishing Company, New York, N.Y., 1949. Translated by John Wermer. MR**0029000** - Daniel Ray,
*Stable processes with an absorbing barrier*, Trans. Amer. Math. Soc.**89**(1958), 16–24. MR**105178**, DOI https://doi.org/10.1090/S0002-9947-1958-0105178-5
E. C. Titchmarsh,

*Introduction to the theory of Fourier integrals*, Oxford, Clarendon Press, 1948.

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© Copyright 1961
American Mathematical Society