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A note on convergence rate of a linearization method for the discretization of stochastic differential equations. (English) Zbl 1221.65020

Summary: This note discusses convergence rate of a linearization method for the discretization of stochastic differential equations with multiplicative noise. The method is to approximate the drift coefficient by the local linearization method and the diffusion coefficient by the Euler method. The mixed method guarantees the approximated process converges to the original one with the rate of convergence \(\Delta t\), where \(\Delta t\) is the time interval of discretization.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)

Software:

sde
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References:

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