Rigorous convergence bounds for stochastic differential equations with application to uncertainty quantification
Prediction via continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we consider a general class of stochastic differential equations and provide rigor...
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| Published in | Physica. D Vol. 481; p. 134742 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.11.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-2789 1872-8022 |
| DOI | 10.1016/j.physd.2025.134742 |
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| Abstract | Prediction via continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we consider a general class of stochastic differential equations and provide rigorous convergence bounds to an analytically solvable approximation. We provide the explicit convergence rate for all moments of a fully non-autonomous model with both multiplicative noise and uncertain initial conditions. Our second main contribution is to extend stochastic sensitivity, a recently introduced uncertainty quantification tool, to arbitrary dimensions and provide a new calculation method that empowers rapid computation. We demonstrate the power and adaptability of our contributions on a diverse set of numerical examples in 1-, 2-, 3-, and 4-dimensions, including providing stochastic sensitivity calculations for an idealised eddy parameterisation of the Gulf Stream. |
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| AbstractList | Prediction via continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we consider a general class of stochastic differential equations and provide rigorous convergence bounds to an analytically solvable approximation. We provide the explicit convergence rate for all moments of a fully non-autonomous model with both multiplicative noise and uncertain initial conditions. Our second main contribution is to extend stochastic sensitivity, a recently introduced uncertainty quantification tool, to arbitrary dimensions and provide a new calculation method that empowers rapid computation. We demonstrate the power and adaptability of our contributions on a diverse set of numerical examples in 1-, 2-, 3-, and 4-dimensions, including providing stochastic sensitivity calculations for an idealised eddy parameterisation of the Gulf Stream. |
| ArticleNumber | 134742 |
| Author | Maclean, John Blake, Liam A.A. Balasuriya, Sanjeeva |
| Author_xml | – sequence: 1 givenname: Liam A.A. orcidid: 0000-0003-2779-494X surname: Blake fullname: Blake, Liam A.A. email: liam.blake@adelaide.edu.au – sequence: 2 givenname: John orcidid: 0000-0002-5533-0838 surname: Maclean fullname: Maclean, John – sequence: 3 givenname: Sanjeeva orcidid: 0000-0002-3261-7940 surname: Balasuriya fullname: Balasuriya, Sanjeeva |
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| Keywords | Uncertainty quantification Multiplicative and time-dependent noise Stochastic differential equations Gaussian approximations Eddy parameterisation |
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