Bharucha-Reid, A. T., 1960, *Elements of Markov Processes and Their Applications*, McGraw-Hill, New York.

Cox, D. R., and Miller, H. D., 1965, *The Theory of Stochastic Processes*, Chapman and Hall, New York.

Bergman,
L. A., and Heinrich,
J. C., 1981, “On the Moments of Time to First Passage of the Linear Oscillator,” Earthquake Eng. Struct. Dyn., 9, pp. 197–204.

Bergman,
L. A., and Heinrich,
J. C., 1982, “On the Reliability of the Linear Oscillator and Systems of Coupled Oscillators,” Int. J. Numer. Methods Eng., 18, pp. 1271–1295.

Sun,
J. Q., and Hsu,
C. S., 1988, “First-Passage Time Probability of Non-Linear Stochastic Systems by Generalized Cell Mapping Method,” J. Sound Vib., 124, pp. 233–248.

Sun,
J. Q., and Hsu,
C. S., 1990, “The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short Time Gaussian Approximation,” ASME J. Appl. Mech., 57, pp. 1018–1025.

Ariaratnam,
S. T., and Pi,
H. N., 1973, “On the First-Passage Time for Envelope Crossing for a Linear Oscillator,” Int. J. Control, 18, pp. 89–96.

Lennox,
W. C., and Fraser,
D. A., 1974, “On the First Passage Distribution for the Envelope of a Non-stationary Narrow-Band Stochastic Process,” ASME J. Appl. Mech., 41, pp. 793–797.

Ariaratnam,
S. T., and Tam,
D. S. F., 1979, “Random Vibration and Stability of a Linear Parametrically Excited Oscillator,” Z. Angew. Math. Mech., 59, pp. 79–84.

Spanos,
P. D., and Solomos,
G. P., 1984, “Barrier Crossing due to Transient Excitation,” J. Eng. Mech., 110, pp. 20–36.

Roberts,
J. B., 1976, “First Passage Probability for Nonlinear Oscillator,” J. Eng. Mech., 102, pp. 851–866.

Roberts,
J. B., 1978, “First-Passage Time for Oscillator With Nonlinear Restoring Forces,” J. Sound Vib., 56, pp. 71–86.

Roberts,
J. B., 1986, “Response of an Oscillator With Nonlinear Damping and a Softening Spring to Non-White Random Excitation,” Probab. Eng. Mech., 1, pp. 40–48.

Roberts,
J. B., 1986, “First-Passage Time for Randomly Excited Nonlinear Oscillator,” J. Sound Vib., 109, pp. 33–50.

Spanos,
P. D., 1982, “Survival Probability of Non-Linear Oscillators Subjected to Broad-Band Random Disturbance,” Int. J. Non-Linear Mech., 17, pp. 303–317.

Zhu, W. Q., and Lei, Y., 1989, “First Passage Time for State Transition of Randomly Excited Systems,” *Proc. 47th Session of International Statistical Institute*, LIII (Invited Papers), Book 3, pp. 517–531.

Cai,
G. Q., and Lin,
Y. K., 1994, “On Statistics of First-Passage Failure,” ASME J. Appl. Mech., 61, pp. 93–99.

Zhu,
W. Q., and Yang,
Y. Q., 1997, “Stochastic Averaging of Quasi-Non-Integrable-Hamiltonian Systems,” ASME J. Appl. Mech., 64, pp. 157–164.

Zhu,
W. Q., Huang,
Z. L., and Yang,
Y. Q., 1997, “Stochastic Averaging of Quasi-Integrable Hamiltonian Systems,” ASME J. Appl. Mech., 64, pp. 975–984.

Zhu,
W. Q., Huang,
Z. L., and Suzuki,
Y., 2002, “Stochastic Averaging and Lyapunov Exponent of Quasi Partially Integrable Hamiltonian Systems,” Int. J. Non-Linear Mech., 37, pp. 419–437.

Zhu,
W. Q., and Huang,
Z. L., 1998, “Stochastic Stability of Quasi-Non-Integrable-Hamiltonian Systems,” J. Sound Vib., 218, pp. 769–789.

Zhu,
W. Q., and Huang,
Z. L., 1999, “Stochastic Hopf Bifurcation of Quasi-Non-Integrable-Hamiltonian Systems,” Int. J. Non-Linear Mech., 34, pp. 437–447.

Zhu,
W. Q., and Huang,
Z. L., 1999, “Lyapunov Exponents and Stochastic Stability of Quasi-Integrable-Hamiltonian Systems,” ASME J. Appl. Mech., 66, pp. 211–217.

Gan,
C. B., and Zhu,
W. Q., 2001, “First-Passage Failure of Quasi-Non-Integrable-Hamiltonian Systems,” Int. J. Non-Linear Mech., 36(2), pp. 209–220.

Zhu,
W. Q., and Ying,
Z. G., 1999, “Optimal Nonlinear Feedback Control of Quasi-Hamiltonian Systems,” Sci. China, Ser. A: Math., Phys., Astron., 42(11), pp. 1213–1219.

Zhu, W. Q., Ying, Z. G., and Soong, T. T., 1999, “Optimal Nonlinear Feedback Control of Structures Under Random Loading,” *Stochastic Structural Dynamics*, B. F. Spencer, Jr., and E. A. Johnson, eds., Balkema, Rotterdam, pp. 141–148.

Zhu,
W. Q., Ying,
Z. G., Ni,
Y. Q., and Ko,
J. M., 2000, “Optimal Nonlinear Stochastic Control of Hysteretic Systems,” J. Eng. Mech., 126, pp. 1027–1032.

Zhu,
W. Q., Ying,
Z. G., and Soong,
T. T., 2001, “An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems,” Nonlinear Dyn., 24, pp. 31–51.

Zhu,
W. Q., and Ying,
Z. G., 2002, “Nonlinear Stochastic Optimal Control of Partially Observable Linear Strucutres, ” Eng. Struct., 24, pp. 333–342.

Khasminskii,
R. Z., 1968, “On the Averaging Principle for Stochastic Differential Ito⁁ Equations,” Kibernetica, 4, pp. 260–279 (in Russian).

Roberts,
J. B., 1978, “First Passage Time for Oscillators With Non-Linear Restoring Forces,” J. Sound Vib., 56, pp. 71–86.