Rigorous convergence bounds for stochastic differential equations with application to uncertainty quantification
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(Published version)
Date
2025
Authors
Blake, L.
Maclean, J.
Balasuriya, S.
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O'Connor, L.
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Journal article
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Physica D : Non-linear phenomena, 2025; 481:134742-1-134742-19
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Liam A.A. Blake, John Maclean, Sanjeeva Balasuriya
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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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© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).