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First passage times for symmetric stable processes in space. (English) Zbl 0104.11203


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[1] R. M. Blumenthal and R. K. Getoor, Some theorems on stable processes, Trans. Amer. Math. Soc. 95 (1960), 263 – 273. · Zbl 0107.12401
[2] 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. · Zbl 0086.33901
[3] S. Bochner and K. Chandrasekharan, Fourier Transforms, Annals of Mathematics Studies, no. 19, Princeton University Press, Princeton, N. J.; Oxford University Press, London, 1949. · Zbl 0065.34101
[4] Joanne Elliott, Absorbing barrier processes connected with the symmetric stable densities, Illinois J. Math. 3 (1959), 200 – 216. · Zbl 0099.12902
[5] 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. · Zbl 0055.36401
[6] R. K. Getoor, Additive functionals of a Markov process, Pacific J. Math. 7 (1957), 1577 – 1591. · Zbl 0080.34803
[7] R. K. Getoor, Markov operators and their associated semi-groups, Pacific J. Math. 9 (1959), 449 – 472. · Zbl 0086.33804
[8] 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. · Zbl 0078.10004
[9] 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. · Zbl 0201.49801
[10] Mark Kac and Harry Pollard, The distribution of the maximum of partial sums of independent random variables, Canadian J. Math. 2 (1950), 375 – 384. · Zbl 0038.08601
[11] 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. · Zbl 0039.07202
[12] Daniel Ray, Stable processes with an absorbing barrier, Trans. Amer. Math. Soc. 89 (1958), 16 – 24. · Zbl 0083.13804
[13] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford, Clarendon Press, 1948. · Zbl 0017.40404
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