Kyoto Journal of Mathematics

The approximate pseudorandom walk accompanied by the pseudostochastic process corresponding to a higher-order heat-type equation

Tadashi Nakajima and Sadao Sato

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Abstract

As is well known, a standard random walk is approximate to the stochastic process corresponding to the heat equation. Lachal constructed the approximate pseudorandom walk which is accompanied by the pseudostochastic process corresponding to an even-order heat-type equation. We have two purposes for this article. The first is to construct the approximate pseudorandom walk which is accompanied by the pseudostochastic process corresponding to an odd-order heat-type equation. The other is to propose a construction method for the approximate pseudorandom walk which is accompanied by the pseudostochastic process corresponding to an even-order heat-type equation. This method is different from that of Lachal.

Article information

Source
Kyoto J. Math., Volume 57, Number 4 (2017), 693-716.

Dates
Received: 11 September 2015
Revised: 4 January 2016
Accepted: 25 May 2016
First available in Project Euclid: 9 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1496973625

Digital Object Identifier
doi:10.1215/21562261-2017-0012

Mathematical Reviews number (MathSciNet)
MR3725258

Zentralblatt MATH identifier
06825575

Subjects
Primary: 60G20: Generalized stochastic processes
Secondary: 35K41: Higher-order parabolic systems 60G18: Self-similar processes 60K40: Other physical applications of random processes

Keywords
stochastic pseudoprocess heat-type equation random walk

Citation

Nakajima, Tadashi; Sato, Sadao. The approximate pseudorandom walk accompanied by the pseudostochastic process corresponding to a higher-order heat-type equation. Kyoto J. Math. 57 (2017), no. 4, 693--716. doi:10.1215/21562261-2017-0012. https://projecteuclid.org/euclid.kjm/1496973625


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References

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