The Existence and Uniqueness of Random Solution to Itô Stochastic Integral Equation

Show more

References

[1] K. Ito, “Stochastic Integral,” Proceedings of the Imperial Academy, Vol. 20, No. 8, 1944, pp. 519-524.
doi:10.3792/pia/1195572786

[2] J. L. Doob, “Stochastic Processes,” Wiley, New York, 1953, pp. 426-432.

[3] Y. Dynkin, “Markov Processes,” Academic Press, New York, 1964, pp. 9-13.

[4] A. Jazwinski, “Stochastic Processes and Filtering Theory. Mathematics in Science and Engineering,” Vol. 64, Academic Press, New York, 1970, pp. 97-105

[5] K. Ito, “On a Stochastic Integral Equation,” Proceedings of the Japan Academy, Vol. 22, No. 2, 1946, pp. 32-35.
doi:10.3792/pja/1195572371

[6] H. P. Mckean, “Stochastic Integrals,” Academic Press, New York, 1969, pp. 21-25.

[7] T. L. Satty, “Modern Nonlinear Equations,” McGrowHill, New York, 1967, pp. 216-226.

[8] L. Gikhmann and A. V. Skorokhod, “Introduction to the Theory of Random Process-Saunders,” Philadehphia, Pennsylvania, 1969, pp. 378-391.

[9] R. L. Stratonovich, “A New Representation for Stochastic Integrals and Equations,” Journal of SLAM Control, Vol. 4, 1966, pp. 362-371.

[10] E. Wong and M. Zakai, “On the Relation between Ordinary and Stochastic Differential Equations,” International Journal of Engineering Science, Vol. 3, No. 2, 1965, pp. 213-229. doi:10.1016/0020-7225(65)90045-5

[11] I. P. Natanson, “Theory of Functions of a Real Variable,” Vol. II, Ungar, New York, 2010.

[12] A. T. Bharucha-Reid, “On the Theory of Random Equations,” Proceedings of Symposia in Applied Mathematics, Vol. 16, 1964, pp. 40-69.

[13] G. Adomain, “Random Operator Equations in Mathematical Physics,” Journal of Mathematical Physics, Vol. 11, No. 3, 1970, pp. 1069-1074. doi:10.1063/1.1665198

[14] G. Adomain, “Linear Random Operator Equations in Mathematical Physics III,” Journal of Mathematical Physics, Vol. 12, No. 9, 1971, pp. 1944-1948.
doi:10.1063/1.1665827

[15] G. Adomain, “Theory of Random Systems,” Transactions of the fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Prague, 31 August-11 September 1965, pp. 205-222.