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On the Boundary Condition of Transport Semigroup

Published online by Cambridge University Press:  22 January 2016

Toitsu Watanabe
Toitsu Watanabe*
Affiliation:
Department of Applied Physics, Nagoya University
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Let S be the product space of finite interval [—r, r] and two points Θ = {θ±1}.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 219 - 241
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Courrege, P., Problemes aux limites elliptiques et principe du maximum, Sém. Bourbaki, 1965/66, n° 302.Google Scholar
[2] Dynkin, E.B., Markov processes, Springer (1964).Google Scholar
[3] Feller, W., The parabolic differential equations and the associated semigroup of transformations, Ann. Math. 55 (1952), 468–519.CrossRefGoogle Scholar
[4] Feller, W., Diffusion processes in one dimension, Trans. Amer. Math. Soc, 77 (1954), 1–31.Google Scholar
[5] Feller, W., On second order differential operators, Ann. Math., 61 (1955), 90–105.Google Scholar
[6] Feller, W., Generalized second order differential operators and their lateral conditions. Illinois J. Math., 1 (1957), 459–504.CrossRefGoogle Scholar
[7] Fukushima, M., K. Ito and S. Watanabe, Diffusion processes, Seminar on Prob., 3 (1960) (Japanese).Google Scholar
[8] Ikeda, N., On the construction of two dimensional diffusion processes satisfying Wentzell’s boundary conditions and its application to boundary value problems, Mem. Coll. Sci. Univ. Kyoto, Ser. A, 33 (1961), 367–427.Google Scholar
[9] Ikeda, N. and Nomoto, H., Transport branching processes, Seminar on Prob., 25 (1966), 63–104 (Japanese).Google Scholar
[10] Ito, K. and McKean, H.P. Jr, Diffusion Processes and their sample paths, Springer (1965).Google Scholar
[11] Sato, K. and Ueno, T., Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ., 4 (1965), 529–605.Google Scholar
[12] Trotter, H:F., Approximation of semigroups on oprators, Pacific Jour. Math., 8 (1958), 887–919.Google Scholar
[13] Watanabe, To., Approximation of uniform transport process on a finite interval to Brownian motion, Nagoya Math. J., 32 (1968), 297–314.CrossRefGoogle Scholar
[14] Wentzell, A.D., On lateral conditions for multi-dimensional diffusion processes, Teor. Veroyat. Primen., 4 (1959), 172–185 (Russian).Google Scholar
[15] Wentzell, A.D., General boundary problems connected with diffusion processes, Uspehi. Mat. Nauk, 15 (1960), 202–204 (Russian).Google Scholar
[16] Wentzell, A.D., Semigroups of operaters corresponding to a generalized differential operator of second order, DAN SSSR, 111, 2 (1956), 269–272 (Russian).Google Scholar