## Kyoto Journal of Mathematics

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

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

Tadashi Nakajima and Sadao Sato

#### 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