El problema del primer retorno para algunos operadores pseudo-diferenciables elípticos sobre los p-adicos

The Problem of the First Passage Time for Some Elliptic Pseudodfferential Operators Over the p-Adics

En este artculo se estudia el problema del primer retorno asociado a
ciertos operadores pseudo-diferenciales elípticos en dimensiones 4 y 2 sobre los
números p-ádicos. Este tipo de problemas esta conectado con ciertos modelos
de sistemas complejos

In this article we study the problem of the rst passage time as-
sociated to certain elliptic pseudodierential operators in dimensions 4 and 2
over the p-adics. This type of problems appeared in connection with certain
models of complex systems.

The Problem of the First Passage Time for Some Elliptic Pseudodifferential Operators Over the p-Adics El problema del primer retorno para algunos operadores pseudo-diferenciables elípticos sobre los p-ádicos LEONARDO FABIO CHACÓN-CORTES¹

¹Centro de Investigación y de Estudios Avanzados del I.P.N., México D.F, México. Email: fchacon@math.cinvestav.mx

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Abstract

In this article we study the problem of the first passage time associated to certain elliptic pseudodifferential operators in dimensions 4 and 2 over the p-adics. This type of problems appeared in connection with certain models of complex systems.

Key words: Random walks, Diffusion, Dynamics of disordered systems, Relaxation of complex systems, p-Adic numbers, Non-archimean analysis.

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2000 Mathematics Subject Classification: 82B41, 82C44, 26E30.

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Resumen

En este artículo se estudia el problema del primer retorno asociado a ciertos operadores pseudo-diferenciales elípticos en dimensiones 4 y 2 sobre los números p-ádicos. Este tipo de problemas está conectado con ciertos modelos de sistemas complejos.

Palabras clave: Caminatas aleatorias, difusión, sistemas dinámicos desordenados, relajación en sistemas complejos, números p-ádicos, análisis no Arquimediano.

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Texto completo disponible en PDF

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References

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[9] E. B. Dynkin, Markov Processes, Vol. I, Springer-Verlag, 1965.

[10] J. Galeano-Peñaloza and W. A. Zúñiga-Galindo, 'Pseudo-Differential Operators with Semi-Quasielliptic Symbols over p-Adic Fields', J. Math. Anal. Appl. 1, 386 (2012), 32-49.

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[17] R. Rammal, G. Toulouse, and M. A. Virasoro, 'Ultrametricity for Physicists', Rev. Modern Phys. 58, (1986), 765-788.

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(Recibido en febrero de 2014. Aceptado en julio de 2014)

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv48n2a04,
    AUTHOR  = {Chacón-Cortes, Leonardo Fabio},
    TITLE   = {{The Problem of the First Passage Time for Some Elliptic Pseudodifferential Operators Over the \boldsymbol{p}-Adics}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2014},
    volume  = {48},
    number  = {2},
    pages   = {191--209}
}

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