A review on stochastic differential equations for applications in hydrology
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 Poissonian impulses. Also discussed are stochastic integration and the derivation of moment equations via the Itô differential rule. The literature of SDE's is reviewed with an emphasis on the more accessible sources.
scientific article; zbMATH DE number 4080542
scientific article