Stochastic Taylor expansion of derivative-free method for stochastic differential equations
Keywords:Stochastic Taylor Method, Stochastic Differential Equations, Stochastic Taylor Expansion
This paper demonstrates a derivation of stochastic Taylor methods for stochastic differential equations (SDEs). The stochastic Taylor series is extended and truncated at certain terms to achieve the order of convergence of stochatsic Taylor methods for SDEs. The systematic derivation of the expansion of stochastic Taylor series formula is presented. Numerical methods of Euler, Milstein scheme and stochastic Taylor methods of order 2.0 are proposed.
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