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- W1565627862 abstract "We present strong approximations with rate of convergence for the solution of a stochastic differential equation of the form $$ dX_t=b(X_t)dt+sigma(X_t)dB^H_t, $$ where $bin C^1_b$, $sigma in C^2_b$, $B^H$ is fractional Brownian motion with Hurst index $H$, and we assume existence of a unique solution with Doss-Sussmann representation. The results are based on a strong approximation of $B^H$ by means of transport processes of Garz'on et al (2009). If $sigma$ is bounded away from 0, an approximation is obtained by a general Lipschitz dependence result of Romisch and Wakolbinger (1985). Without that assumption on $sigma$, that method does not work, and we proceed by means of Euler schemes on the Doss-Sussmann representation to obtain another approximation, whose proof is the bulk of the paper." @default.
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- W1565627862 date "2011-09-01" @default.
- W1565627862 modified "2023-09-27" @default.
- W1565627862 title "Approximations of fractional stochastic differential equations by means of transport processes" @default.
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- W1565627862 doi "https://doi.org/10.31390/cosa.5.3.01" @default.
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