First passage times for symmetric stable processes in space

Getoor, R. K.

doi:10.1090/S0002-9947-1961-0137148-5

First passage times for symmetric stable processes in space
HTML articles powered by AMS MathViewer

by R. K. Getoor

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

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

PDF | Request permission

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
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 Co., 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, N.Y., 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 10.4153/cjm-1950-034-9
Wilhelm Magnus and Fritz Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, Chelsea Publishing Co., 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 10.1090/S0002-9947-1958-0105178-5

Introduction to the theory of Fourier integrals