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with initial condition <math>\mathbf{x}(t_{0})=\mathbf{x}_{0}</math>, where the drift coefficient <math>\mathbf{f}</math> and the diffusion coefficient <math>\mathbf{g}_{i}</math> are differentiable functions, and <math>\mathbf{w=(\mathbf{w}}^{1},\ldots ,\mathbf{w}
^{m}\mathbf{)}</math> is an ''m''-dimensional standard [[Wiener process]].
=== Local Linear discretization ===
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\right.</math>
<math>\mathbf{f}_{\mathbf{x}}, \mathbf{f}_{t}</math> denote the partial derivatives of <math>\mathbf{f}</math> with respect to the variables <math>\mathbf{x}</math> and '''''t''''', respectively, and <math>\mathbf{f}_{\mathbf{xx}}</math> the Hessian matrix of <math>\mathbf{f}</math> with respect to <math>\mathbf{x}</math>. The strong Local Linear discretization <math>\mathbf{z}_{n+1}</math> [[Convergence of random variables|converges]] with order<math>\mathbb{\gamma } \quad (=1,1.5)</math> to the solution of '''(14)'''
=== High Order Local Linear discretizations ===
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