References
Anderson, M. W. (1966). Stochastic Integral Equations, Doctoral thesis, University of Tennessee, Knoxville.
Bharucha-Reid, A. T. (1960). On random solutions of Fredholm integral equations,Bull. Amer. Math. Soc.,66, 104–109.
Bharucha-Reid, A. T. (1964). On the theory of random equations,Proc. Symp. Appl. Math., American Math. Soc., Providence, R. I.,16, 40–69.
Bharucha-Reid, A. T. (1972).Random Integral Equations, Academic Press.
Doob, J. L. (1953).Stochastic Processes, Wiley, New York.
Milton, J. Susan, Padgett, W. J. and Tsokos, Chris P. (1972). On the existence and uniqueness of a random solution to a perturbed random integral equation of the Fredholm type.SIAM J. Appl. Math.,22, 194–208.
Morozan, T. (1967). Stability of linear systems with random parameters,J. Differential Equations,3, 170–178.
Padgett, W. J. and Tsokos, Chris P. (1972). On a stochastic integral equation of the Fredholm type.Z. Wahrscheinlichkeisth.,23, 22–31.
Padgett, W. J. and Tsokos, Chris P. (1970). On a semi-stochastic model arising in a biological system,Math. Biosci.,9, 105–117.
Padgett, W. J. and Tsokos, Chris P. (1971). On the existence of a solution of a stochastic integral equation in turbulence theory,J. Math. Phys.,12, 210–212.
Padgett, W. J. and Tsokos, Chris P. (1971). On a stochastic integral equation of the Volterra type in telephone traffic theory,J. Appl. Prob.,8, 269–275.
Skorokhod, A. V. (1965).Studies in the Theory of Random Processes, Addison-Wesley, Reading, Massachusetts.
Tsokos, Chris P. (1969). On a stochastic integral equation of the Volterra type,Math. Systems Theor.,3, 222–231.
Tsokos, Chris P. (1971). The method of V. M. Popov for differential systems with random parameters,J. Appl. Prob.,8, 298–310.
Tsokos, Chris P. (1969). On the classical stability theorem of Poincaré-Lyapunor with random parameters,Proc. Japan Acad.,45, 780–787.
Tsokos, Chris P. (1969). On some nonlinear differential systems with random parameters,IEEE Proc. Third Annual Princeton Conf. on Inf. Sciences and Systems, 228–234.
Tsokos, Chris P. and Padgett, W. J. (1971). Random Integral Equations with Applications to Stochastic Systems,Lecture Notes in Mathematics, Vol. 233, Springer-Verlag, Berlin-Heidelberg-New York.
Yosida, K. (1965).Functional Analysis, Springer-Verlag, Berlin-Heidelberg-New York.
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This research was partially supported by the United States Air Force Office of Scientific Research, under Grant No. AFOSR-74-2711.
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Rao, A.N.V., Tsokos, C.P. On the existence of a random solution to a nonlinear perturbed stochastic integral equation. Ann Inst Stat Math 28, 99–109 (1976). https://doi.org/10.1007/BF02504733
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DOI: https://doi.org/10.1007/BF02504733