Mean-square contractivity of stochastic $\theta$-methods
| Autor: | Stefano Di Giovacchino, Raffaele D'Ambrosio |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mean square
Numerical Analysis Applied Mathematics Nonlinear stability Nonlinear stochastic differential equations Dynamics (mechanics) 01 natural sciences Stochastic theta-methods 010305 fluids & plasmas Stochastic differential equation Stochastic dynamics Exponential growth Modeling and Simulation 0103 physical sciences Exponential mean-square contractivity Stochastic differential equations Applied mathematics Mathematics - Numerical Analysis 010306 general physics Selection (genetic algorithm) Mathematics |
| Popis: | The paper is focused on the nonlinear stability analysis of stochastic θ -methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays, i.e., a mean-square contractive behaviour is visible along the stochastic dynamics. We aim to make the same property visible also along the numerical dynamics generated by stochastic θ -methods: this issue is translated into sharp stepsize restrictions depending on parameters of the problem, here accurately estimated. A selection of numerical tests confirming the effectiveness of the analysis and its sharpness is also provided. |
| Databáze: | OpenAIRE |
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