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Approximate solution of random ordinary differential equations

Published online by Cambridge University Press:  01 July 2016

William E. Boyce
William E. Boyce*
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York
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Abstract

This is a largely expository paper on approximate methods of solving random ordinary differential equations, with an emphasis on direct numerical methods. Two methods are discussed in some detail and several others are mentioned briefly.

Keywords

RANDOM DIFFERENTIAL EQUATIONSSTOCHASTIC ANALYSIS
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 1 , March 1978 , pp. 172 - 184
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Kohler, W. E. and Boyce, W. E. (1974) A numerical analysis of some first order stochastic initial value problems. SIAM J. Appl. Maths 27, 167–179.CrossRefGoogle Scholar
[2] Kohler, W. E. (1972) A numerical approach to the solution of some stochastic differential equations. Doctoral dissertation, Rensselaer Polytechnic Institute, Troy, New York.Google Scholar
[3] Barry, M. R. (1976) Numerical solution of a class of random boundary value problems. Doctoral dissertation, Rensselaer Polytechnic Institute, Troy, New York.Google Scholar
[4] Barry, M. R. and Boyce, W. E. (1977) Numerical solution of a class of random boundary value problems. J. Math. Anal. Appl. To appear.Google Scholar
[5] Onicescu, O. and Istratescu, V. I. (1975) Approximation theorems for random functions. Rend. Mat. (6) 8, 65–81.Google Scholar
[6] Papoulis, A. (1965) Truncated Taylor expansion of a stochastic process. IEEE Trans. Inf. Theory IT-11, 593–594.Google Scholar
[7] Rao, N. J., Bornker, J. D. and Ramkrishna, D. (1974) Numerical solution of Ito integral equations. SIAM J. Control 12, 124–139.Google Scholar
[8] Mil'shtein, G. N. (1974) Approximate integration of stochastic differential equations. Theory Prob. Appl. 19, 557–562.Google Scholar
[9] Lax, M. D. and Boyce, W. E. (1976) The method of moments for linear random initial value problems. J. Math. Anal. Appl. 53, 111–132.Google Scholar
[10] Lax, M. D. (1976) The method of moments for linear random boundary value problems. SIAM J. Appl. Math. 31, 62–83.Google Scholar
[11] Lax, M. D. (1977) Method of moments approximate solutions of random linear integral equations. J. Math. Anal. Appl. 58, 46–55.Google Scholar
[12] Elrod, M. (1973) Numerical methods for the solution of stochastic differential equations. Doctoral dissertation, University of Georgia, Athens, Georgia.Google Scholar