## Kyoto Journal of Mathematics

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

#### 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
Revised: 4 January 2016
Accepted: 25 May 2016
First available in Project Euclid: 9 June 2017

https://projecteuclid.org/euclid.kjm/1496973625

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

Mathematical Reviews number (MathSciNet)
MR3725258

Zentralblatt MATH identifier
06825575

#### 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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