A review on stochastic differential equations for applications in hydrology |
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| Authors: | B A Bodo M E Thompson T E Unny |
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| Institution: | (1) Ontario Ministry of the Environment, M4V 1P5 Toronto, Ontario, Canada;(2) Dept. of Statistics and Actuarial Science, University of Waterloo, N2L 3G1, Ontario, Canada;(3) Dept. of Systems Design Engineering, University of Waterloo, N2L 3G1, Ontario, Canada |
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| Abstract: | Fundamentals of the theory of stochastic calculus and stochastic differential equations (SDE's) which are finding increasing application in water resources engineering are reviewed. The basics of probability theory, mean square calculus and the Wiener, white Gaussian and compound Poisson processes are given in preparation for a discussion of the general Itô SDE with drift, diffusion and jump discontinuity terms driven by Gaussian white noise and compound Poissionian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The lierature of SDE's is reviewed with an emphasis on the more accessible sources. |
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| Keywords: | Stochastic differential equations Itô calculus Stratovovich integrals Jump integrals |
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