Strong and weak orders in averaging for SPDEs

By Charles-Edouard Br'ehier. 2012

129 citations recorded by the source corpus.

Abstract We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time scale. We prove that the slow component of the solution of the system converges towards the solution of the averaged equation with an order of convergence 1/2 in a strong sense–approximation of trajectories–and 1 in a weak sense–approximation of laws. These orders turn out to be the same as for the SDE case.

Subfields: Computational Theory and Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/c26c6174f4815c91093097696525b78fbcd6b78d

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In Computational Theory and Mathematics

In Finance

In Modeling and Simulation

Citations in the corpus

Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component (2018, methodology): “This coincides with the orders of convergence obtained in [3], where no stochastic perturbation is acting in the slow component, i.”
Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles (2017, background): “On the other hand, Bréhier [4] derived explicit convergence rates in both strong and weak convergences for averaging of stochastic parabolic equations.”
Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs (2021, background): “For example, Dong et al. [15] studied the strong and weak averaging principle for stochastic Burgers equations, Bréhier [9, 10] gave the strong and weak orders in averaging for stochastic evolution equation of parabolic type with slow and fast time-scales.”
Strong convergence order for slow–fast McKean–Vlasov stochastic differential equations (2019, methodology): “, [20, 21, 25, 34] for the finite dimensional case, and [3, 4] for the infinite dimensional case).”