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Stochastic waves. (English) Zbl 0513.60072

MSC:
60J35 Transition functions, generators and resolvents
60J25 Continuous-time Markov processes on general state spaces
60J60 Diffusion processes
35J25 Boundary value problems for second-order elliptic equations
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[1] E. B. Dynkin, Markov processes. Vols. I, II, Translated with the authorization and assistance of the author by J. Fabius, V. Greenberg, A. Maitra, G. Majone. Die Grundlehren der Mathematischen Wissenschaften, Bände 121, vol. 122, Academic Press Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. · Zbl 0132.37901
[2] E. B. Dynkin, Harmonic functions associated with several Markov processes, Adv. in Appl. Math. 2 (1981), no. 3, 260 – 283. · Zbl 0479.60057 · doi:10.1016/0196-8858(81)90007-5 · doi.org
[3] O. D. Kellogg, Foundations of potential theory, Dover, New York, 1953. · Zbl 0053.07301
[4] Olga A. Ladyzhenskaya and Nina N. Ural’tseva, Linear and quasilinear elliptic equations, Translated from the Russian by Scripta Technica, Inc. Translation editor: Leon Ehrenpreis, Academic Press, New York-London, 1968. · Zbl 0164.13002
[5] Carlo Miranda, Partial differential equations of elliptic type, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, Springer-Verlag, New York-Berlin, 1970. Second revised edition. Translated from the Italian by Zane C. Motteler.
[6] Frank Spitzer, Some theorems concerning 2-dimensional Brownian motion, Trans. Amer. Math. Soc. 87 (1958), 187 – 197. · Zbl 0089.13601
[7] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501
[8] Robert Joseph Vanderbei, Toward a stochastic calculus for several Markov processes, Adv. in Appl. Math. 4 (1983), no. 2, 125 – 144. · Zbl 0519.60077 · doi:10.1016/0196-8858(83)90007-6 · doi.org
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