Journal of Nonlinear Mathematical Physics

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Volume 18, Issue 3, September 2011, Pages 427 - 441

Linearization of a Second-Order Stochastic Ordinary Differential Equation

Authors
Sergey V. Meleshko*, Eckart Schulz†
School of Mathematics, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand
Center of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand
Received 31 January 2011, Accepted 14 March 2011, Available Online 7 January 2021.
DOI
10.1142/S1402925111001696How to use a DOI?
Keywords
Brownian motion; linearization; stochastic ordinary differential equation
Abstract

Necessary and sufficient conditions which allow a second-order stochastic ordinary differential equation to be transformed to linear form are presented. The transformation can be chosen in a way so that all but one of the coefficients in the stochastic integral part vanish. The linearization criteria thus obtained are used to determine the general form of a linearizable Langevin equation.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 3
Pages
427 - 441
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001696How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Sergey V. Meleshko
AU  - Eckart Schulz
PY  - 2021
DA  - 2021/01/07
TI  - Linearization of a Second-Order Stochastic Ordinary Differential Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 427
EP  - 441
VL  - 18
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001696
DO  - 10.1142/S1402925111001696
ID  - Meleshko2021
ER  -