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A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field

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  • Kaneko, Hiroshi

Abstract

In this paper, we will present a method to construct a spatially inhomogeneous process on the p-adic number field. Secondly, we will modify the definition of the derivative of real-valued function on the field, hinted by the Fourier transformation. As a result, we can introduce a class of spatially inhomogeneous modified stable processes, which cannot be obtained by the transformation by multiplicative functional. Lastly, recurrence and transience criteria for the non-local Dirichlet spaces will be presented.

Suggested Citation

  • Kaneko, Hiroshi, 2000. "A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 161-174, July.
    • Handle: RePEc:eee:spapps:v:88:y:2000:i:1:p:161-174
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    References listed on IDEAS

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    1. Albeverio, Sergio & Karwowski, Witold, 1994. "A random walk on p-adics--the generator and its spectrum," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 1-22, September.
    2. Albeverio, Sergio & Karwowski, Witold & Zhao, Xuelei, 1999. "Asymptotics and spectral results for random walks on p-adics," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 39-59, September.
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    Cited by:

    1. Hiroshi Kaneko & Xuelei Zhao, 2006. "Transition Semi–groups on a Local Field Induced by Galois Group and their Representation," Journal of Theoretical Probability, Springer, vol. 19(1), pages 221-234, January.

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