Abstract
The theory of stochastic differential equations is introduced in this chapter. The emphasis is on Ito stochastic differential equations, for which an existence and uniqueness theorem is proved and the properties of their solutions investigated. Techniques for solving linear and certain classes of nonlinear stochastic differential equations are presented, along with an extensive list of explicitly solvable equations. Finally, Stratonovich stochastic differential equations and their relationship to Ito equations are examined.
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Bibliographical Notes
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Kloeden, P.E., Platen, E. (1992). Stochastic Differential Equations. In: Numerical Solution of Stochastic Differential Equations. Applications of Mathematics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12616-5_4
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DOI: https://doi.org/10.1007/978-3-662-12616-5_4
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