Abstract
Let G be infinitesimal generator of a Feller transition semigroup on a compact C∞ manifold M with boundary. Assume that G is defined by means of a sufficiently smooth integrodifferential elliptic boundary system of Ventcel. Let U be an open subset of M/∂M. Then the operator
uniquely determines the canonical cadlag Markov process corresponding to G before its first exit time from U. This statement is formulated and proved in rigorous measure theoretical language.
Keywords
- Probability Measure
- Open Subset
- Elliptic System
- Exit Time
- Infinitesimal Generator
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References
P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, Inc., 1968.
R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, 1968.
J.-M. Bony, Ph. Courrége et P. Priouret, Semi-groupes de Feller sur une variété a bord compacte et problémes aux limites intégro-différentielles du second ordre donnant lieu au principe du maximum, Ann. Inst. Fourier 18, 2 (1968), p. 369–521.
E.B. Dynkin, Markov Processes, Vol. I, Springer-Verlag, 1965.
S.N. Ethiér and T.G. Kurtz, Markov Processes, Characterization and Convergence, John Wiley and Sons, 1986.
I.I. Gichman and A.V. Skorochod, Theory of Stochastic Processes, Vol. I (in russian), "Nauka", Moscow, 1971.
N. Ikeda and S. Watanabe, On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2 (1962), p. 79–95.
K. Itô and H. Mc Kean, Diffusion processes and their sample paths, Springer-Verlag, 1965.
J. Kisyński, On a formula of N. Ikeda and S. Watanabe concerning the Lévy kernel, p. 260–279 in "Probability Measures on Groups VII", Lecture Notes in Mathematics, Vol. 1064, Springer-Verlag, 1984.
J. Kisyński, On jumps of paths of Markov processes, p.130–145 in "Probability Measures on Groups VIII", Lecture Notes in Mathematics, Vol. 1210, Springer-Verlag, 1986.
K. Sato and T. Ueno, Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ. 4 (1965), p. 529–605.
W. von Waldenfels, Fast positive Operatoren, Zeitschrift für Wahrscheinlichkeitstheorie 4 (1965), p. 159–174.
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© 1989 Springer-Verlag
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Kisyński, J. (1989). Localizations of Feller infinitesimal generators and uniqueness of corresponding killed processes. In: Heyer, H. (eds) Probability Measures on Groups IX. Lecture Notes in Mathematics, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087852
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DOI: https://doi.org/10.1007/BFb0087852
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Print ISBN: 978-3-540-51401-5
Online ISBN: 978-3-540-46206-4
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