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Stochastic modelling in fluid dynamics: Itô versus Stratonovich
Suppose the observations of Lagrangian trajectories for fluid flow in some physical situation can be modelled sufficiently accurately by a spatially correlated Itô stochastic process (with zero mean) obtained from data which is taken in fixed Eulerian space. Suppose we also want to apply Hamilton’s...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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The Royal Society Publishing
2020
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7277131/ https://www.ncbi.nlm.nih.gov/pubmed/32518504 http://dx.doi.org/10.1098/rspa.2019.0812 |
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author | Holm, Darryl D. |
author_facet | Holm, Darryl D. |
author_sort | Holm, Darryl D. |
collection | PubMed |
description | Suppose the observations of Lagrangian trajectories for fluid flow in some physical situation can be modelled sufficiently accurately by a spatially correlated Itô stochastic process (with zero mean) obtained from data which is taken in fixed Eulerian space. Suppose we also want to apply Hamilton’s principle to derive the stochastic fluid equations for this situation. Now, the variational calculus for applying Hamilton’s principle requires the Stratonovich process, so we must transform from Itô noise in the data frame to the equivalent Stratonovich noise. However, the transformation from the Itô process in the data frame to the corresponding Stratonovich process shifts the drift velocity of the transformed Lagrangian fluid trajectory out of the data frame into a non-inertial frame obtained from the Itô correction. The issue is, ‘Will non-inertial forces arising from this transformation of reference frames make a difference in the interpretation of the solution behaviour of the resulting stochastic equations?’ This issue will be resolved by elementary considerations. |
format | Online Article Text |
id | pubmed-7277131 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-72771312020-06-08 Stochastic modelling in fluid dynamics: Itô versus Stratonovich Holm, Darryl D. Proc Math Phys Eng Sci Research Article Suppose the observations of Lagrangian trajectories for fluid flow in some physical situation can be modelled sufficiently accurately by a spatially correlated Itô stochastic process (with zero mean) obtained from data which is taken in fixed Eulerian space. Suppose we also want to apply Hamilton’s principle to derive the stochastic fluid equations for this situation. Now, the variational calculus for applying Hamilton’s principle requires the Stratonovich process, so we must transform from Itô noise in the data frame to the equivalent Stratonovich noise. However, the transformation from the Itô process in the data frame to the corresponding Stratonovich process shifts the drift velocity of the transformed Lagrangian fluid trajectory out of the data frame into a non-inertial frame obtained from the Itô correction. The issue is, ‘Will non-inertial forces arising from this transformation of reference frames make a difference in the interpretation of the solution behaviour of the resulting stochastic equations?’ This issue will be resolved by elementary considerations. The Royal Society Publishing 2020-05 2020-05-27 /pmc/articles/PMC7277131/ /pubmed/32518504 http://dx.doi.org/10.1098/rspa.2019.0812 Text en © 2020 The Authors. http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Research Article Holm, Darryl D. Stochastic modelling in fluid dynamics: Itô versus Stratonovich |
title | Stochastic modelling in fluid dynamics: Itô versus Stratonovich |
title_full | Stochastic modelling in fluid dynamics: Itô versus Stratonovich |
title_fullStr | Stochastic modelling in fluid dynamics: Itô versus Stratonovich |
title_full_unstemmed | Stochastic modelling in fluid dynamics: Itô versus Stratonovich |
title_short | Stochastic modelling in fluid dynamics: Itô versus Stratonovich |
title_sort | stochastic modelling in fluid dynamics: itô versus stratonovich |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7277131/ https://www.ncbi.nlm.nih.gov/pubmed/32518504 http://dx.doi.org/10.1098/rspa.2019.0812 |
work_keys_str_mv | AT holmdarryld stochasticmodellinginfluiddynamicsitoversusstratonovich |