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Notes on energy for space-time processes over Lévy processes

Published online by Cambridge University Press:  22 January 2016

Mamoru Kanda
Mamoru Kanda*
Affiliation:
Department of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305, Japan
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Let X = (Xt, 0 ≤ t < ∞) be a Lévy process on the Euclidean space Rd, that is, a process on Rd with stationary independent increments which has right continuous paths with left limits. We denote by Px the probability measure such that PX(X0 = x) = 1 and by Ex the expectation relative to Px. The process is characterized by the exponent Ψ through

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Type
Research Article
Information
Nagoya Mathematical Journal , Volume 122 , June 1991 , pp. 63 - 74
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[1] Blumenthal, R. G. and Getoor, R. K., Markov Processes and Potential Theory, Academic Press, New York, 1968.Google Scholar
[2] Bochner, S., Harmonic Analysis and Theory of Probability, Berkeley: Univ. of California Press 1955.CrossRefGoogle Scholar
[3] Fitzsimmons, P. J., Remarks on a paper of Kanda, (private communication), (1989).Google Scholar
[4] Hawkes, J., Potential theory of Levy processes, Proc. London Math. Soc., (3) 38 (1979), 335–352.CrossRefGoogle Scholar
[5] Kanda, M., Two theorems on capacity for Markov processes with stationary independent increments, Z. Wahrsch. Verw. Gebiete, 35 (1976), 159–165.CrossRefGoogle Scholar
[6] Kanda, M., Characterizations of semipolar sets for processes with stationary independent increments, Z. Wahrsch. Verw. Gebiete, 42 (1978), 141–154.CrossRefGoogle Scholar
[7] Kanda, M., Characterization of semipolar sets for Levy processes by Fourier transform of measures, Surikaiseki Kenkyusho Kokyuroku, 502 (1983), 161–170.Google Scholar
[8] Kanda, M., A note on capacitary measures of semipolar sets, The Annals of Probability, (1) 17 (1989), 379–384.Google Scholar
[9] Kanda, M., A note on a characterization of semipolar sets, Abstracts, Singapore Prob. Conference (1989).Google Scholar
[10] Pop-Stojanovic, Z. R., Energy in Markov processes, Functional analysis, (II) (Dubrovnik 1985), Lecture Notes in Math., 1242 (1987), 374–395.Google Scholar
[11] Rao, M., On polar sets for Lévy processes, J. London Math. Soc., (2) 35 (1987), 569–576.Google Scholar
[12] Rao, M., Hunt’s hypothesis for Levy processes, Proc. Amer. Math. Soc., (2) 104 (1988), 621–624.Google Scholar
[13] Sharpe, M., General Theory of Markov Processes, Academic Press, San Diego, 1988.Google Scholar
[14] Zabczyk, J., A note on semipolar sets for processes with independent increments, Winter School on Probability, Karpacz, Poland, Lecture Notes in Math., 472 (1975) 277–283.Google Scholar