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- W2045386145 abstract "There is a lack of appropriate replication of the asymptotical behaviour of stationary stochastic differential equations solved by numerical methods. The paper illustrates this fact with the stationary Ornstein-Uhlenbeck process and family of implicit Euler methods. For description of occuring bias, notions of asymptotical p-th. mean, mean, mean square and equilibrium preservation are introduced, due to stochasticity of stationary law. Only the trapezoidal formula among these methods is optimal in the sense of replication of exact asymptotical behaviour. We also discuss the general probabilistic law of linear Euler methods. The results can be useful for implementation of stochastic-numerical algorithms (e.g. for linear-implicit methods) in several disciplines of Natural and Environmental Sciences" @default.
- W2045386145 created "2016-06-24" @default.
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- W2045386145 date "1999-01-01" @default.
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- W2045386145 title "Preservation of probabilistic laws through Euler methods for ornstein-uhlenbeck process" @default.
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- W2045386145 doi "https://doi.org/10.1080/07362999908809613" @default.
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