Strong and weak orders in averaging for SPDEs
Copyright policy )Strong and weak orders in averaging for SPDEs
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 is 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.
- University of Rennes France
- French National Centre for Scientific Research France
- University of Rennes 1 France
- Agrocampus Ouest France
- L'Institut Agro France
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Numerical Analysis, Averaging Principle, Stochastic Partial Differential Equations, Averaging of perturbations for nonlinear problems in mechanics, Applied Mathematics, Probability (math.PR), Stochastic partial differential equations, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 60H15,70K65,70K70, Strong and Weak Approximation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Averaging principle, Stochastic partial differential equations (aspects of stochastic analysis), Modelling and Simulation, FOS: Mathematics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Strong and weak approximations, Probability
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Numerical Analysis, Averaging Principle, Stochastic Partial Differential Equations, Averaging of perturbations for nonlinear problems in mechanics, Applied Mathematics, Probability (math.PR), Stochastic partial differential equations, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 60H15,70K65,70K70, Strong and Weak Approximation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Averaging principle, Stochastic partial differential equations (aspects of stochastic analysis), Modelling and Simulation, FOS: Mathematics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Strong and weak approximations, Probability
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