Abstract
Silverstein’s formula ([5]) for Green operators of absorbing Levy processes on [0, ∞) is proved, without the assumption of the absolute continuity of Green measures, by making use of the Wiener-Hopf factorization for Lévy processes.
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References
Fristedt, B., Sample functions of stochastic processes with stationary independent increments, Adv. Probab. 3 (1973), 241–396.
Greenwood, P. and Pitman, J., Fluctuation identities for Lévy processes and splitting at the maximum, Adv. Appl. Probab. 12 (1980), 893–902.
Pecherskii, E. A. and Rogozin, B. A., On joint distributions of random variables associated with fluctuations of a process with independent increments, Theor. Probab. Appl. 14 (1969), 410–423.
Sato, K., “Processes with Independent Increments (in Japanese),” Kinokuniya, Tokyo, 1990.
Silverstein, M. L., Classification of coharmonic and coinvariant functions for a Lévy process, Ann. Probab. 8 (1980), 539–575.
Spitzer, F., “Principles of Random Walk,” Van Nostrand, New York, 1964.
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© 1993 Springer-Verlag New York, Inc.
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Tanaka, H. (1993). Green Operators of Absorbing Lévy Processes on the Half Line. In: Cambanis, S., Ghosh, J.K., Karandikar, R.L., Sen, P.K. (eds) Stochastic Processes. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7909-0_35
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DOI: https://doi.org/10.1007/978-1-4615-7909-0_35
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4615-7911-3
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