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Asymptotic Behavior of Skew Conditional Heat Kernels on Graph Networks

Published online by Cambridge University Press:  20 November 2018

Tatsuya Okada
Tatsuya Okada*
Affiliation:
Department of Mathematics and Statistics, Fukushima Medical College, 1 Hikarigaoka, Fukushima, 960-12, Japan
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Abstract

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In this note, we will consider the heat propagation on locally finite graph networks which satisfy a skew condition on vertices (See Definition of Section 2). For several periodic models, we will construct the heat kernels Pt with the skew condition explicitly, and derive the decay order of Pt as time goes to infinity.

Keywords

58G1168E10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 863 - 878
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Gaveau, B. and Okada, M., Differential forms and heat diffusion on one dimensional singular varieties, Bull. Sci. Math. 115(1991), 61–80.Google Scholar
2. Gaveau, B., Okada, M. and Okada, T.., Explicit heat kernels on graphs and spectral analysis, Several Complex Variables, Math. Notes 38(1991), Princeton Univ. Press.Google Scholar
3. Harrison, J. M. and Shepp, L. A., On skew Brownian motion, Ann. Prob. 9(1981), 309–313.Google Scholar
4. Ikeda, N. and Watanabe, S., The local structure of a class of diffusions and related problems, Proc. Second Japan-USSR Symp. Prob. Theor., Lecture Notes in Math. 330, Springer-Verlag, Berlin, 1973, 124–169.Google Scholar
5. Ito, K. and Mckean, H. P. Jr., Diffusion processes and their sample paths, Springer-Verlag, Berlin, 1965.Google Scholar
6. Okada, M., Sekiguchi, T. and Shiota, Y., Heat kernels on infinite graph networks and deformed Sierpinski gaskets, Japan J. Appl. Math. 7(1990), 527–543.Google Scholar
7. Portenko, N. I., Generalized diffusion processes, Lecture Notes in Math. 550, Springer-Verlag, Berlin, 1976, 500–523.Google Scholar
8. Rosenkrantz, W., Limit theorems for solutions to a class of stochastic differential equations, Indiana Math. J. 24(1975), 613–625.Google Scholar
9. Walsh, J. B., A diffusion with a discontinuous local time, Astérisque, 52-53(1978), 37–45.Google Scholar