Geodesic
Peculiarities of the trajectories of an oscillator excited by a stationary random force
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1982), pp. 85-92

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Let a linear oscillator be affected by a Gaussian stationary process with $$ \int_0^\infty t|R(t)|\,dt\infty, $$ where $R(t)$ is its correlation function. Then almost for sure the amplitude becomes, first, arbitrarily large and, then, arbitrarily small. 
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     author = {N. I. Mikhailov},
     title = {Peculiarities of the trajectories of an oscillator excited by a stationary random force},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {85--92},
     publisher = {mathdoc},
     number = {3},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_3_a20/}
}
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N. I. Mikhailov. Peculiarities of the trajectories of an oscillator excited by a stationary random force. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1982), pp. 85-92. http://geodesic.mathdoc.fr/item/VMUMM_1982_3_a20/