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References
Blumenthal, R. M.: An extended Markov property. Trans. Amer. math. Soc. 85, 52–72 (1957).
—, Getoor, R. K.: Markov processes and potential theory. New York: Academic Press 1968.
— —: Sample functions of stochastic processes with stationary independent increments. J. Math. Mech. 10, 493–515 (1961).
Hewitt, E., Savage, L.: Symmetric measures on Cartesian products. Trans. Amer. math. Soc. 80, 470–501 (1955).
Jain, N., Pruitt, W. E.: The correct measure function for the graph of a transient stable process. Z. Wahrscheinlichkeitstheorie verw. Geb. 9, 131–138 (1968).
Khinchine, A.: Zwei SÄtze über stochastische Prozesse mit stabilen Verteilungen. Mat. Sbornik 45, 577–584 (1938) (Russian, German summary).
- Sur la croissance locale des processes stochastique homogenes à acroissments independents. Izvestia Akad. Nauk SSSR, Ser. math. 487–508 (1939).
Levy, Paul: Théorie de l'addition des variables aleatoires. Paris 1937.
Pruitt, W. E., Taylor, S. J.: Sample path properties of processes with stable components. Z. Wahrscheinlichkeitstheorie verw. Geb. 12, 267–289 (1969).
Skorohod, A. V.: Asymptotic formulas for stable distribution laws. Select. Transl, math. Statist. Probab. 1, 157–162 (1961).
Takeuchi, J.: A local asymptotic law for the transient stable process. Proc. Japan Acad. 40, 141–144 (1964).
—: On the sample paths of the symmetric stable processes in spaces. J. math. Soc. Japan 16, 109–127 (1964).
Taylor, S. J.: Sample path properties of a transient stable process. J. Math. Mech. 16, 1229–1246 (1967).
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The author was partially supported by the National Science Foundation under Grant No. GP 1177–2.
This research was part of the author's doctoral dissertation at the University of Minnesota. Professor W. E. Pruitt, as thesis adviser, provided frequent encouragement and many helpful suggestions which are gratefully acknowledged. Professor B. E. Fristedt of Minnesota helped to foster the author's interest in probability through course work and a number of conversations; the argument in Section 4 is patterned after Professor Fristedt's work for the symmetric stable case.
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Hendricks, W.J. Lower envelopes near zero and infinity for processes with stable components. Z. Wahrscheinlichkeitstheorie verw Gebiete 16, 261–278 (1970). https://doi.org/10.1007/BF00535132
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DOI: https://doi.org/10.1007/BF00535132