Effect of white noise on the \(d\)-dimensional harmonic oscillator (Q1378140)
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scientific article; zbMATH DE number 1113589
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Effect of white noise on the \(d\)-dimensional harmonic oscillator |
scientific article; zbMATH DE number 1113589 |
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Effect of white noise on the \(d\)-dimensional harmonic oscillator (English)
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3 March 1998
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The author studies the \(d\)-dimensional isotropic harmonic oscillator perturbed by small in some sense random term \(dW_tx_t\), where \(W_t\) denotes the Brownian motion. He obtains explicit formulas for the limit of Lyapunov type exponents \(t^{-1}\ln E(\| x_t\|^2)\) and almost sure limit of \(t^{-1}\ln(\| x_t\|^2+\| v_t\|^2)\), when the small parameter tends to zero.
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isotropic harmonic oscillator
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Lyapunov exponent
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perturbation method
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0.8878016
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0.87118036
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0.8686738
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0.86532605
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0.8607825
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