Formal power-series expansion of the stochastically perturbed cubic anharmonic oscillator yields coefficients that solve perturbed Lamé equations, solved explicitly via Jacobi elliptic functions, together with a probability lower bound for closeness to the deterministic periodic solution.
Volker, Four Remarks on Eigenvalues of Lam´ e’s Equation, Analysis and Appli- cations 2 (2004) 161-175
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Stochastic perturbation of a cubic anharmonic oscillator
Formal power-series expansion of the stochastically perturbed cubic anharmonic oscillator yields coefficients that solve perturbed Lamé equations, solved explicitly via Jacobi elliptic functions, together with a probability lower bound for closeness to the deterministic periodic solution.