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- W2964129611 abstract "We consider the one-dimensional squared Bessel process given by the stochastic differential equation (SDE) begin{align*} dX_t = 1,dt + 2sqrt{X_t},dW_t, quad X_0=x_0, quad tin[0,1], end{align*} and study strong (pathwise) approximation of the solution $X$ at the final time point $t=1$. This SDE is a particular instance of a Cox-Ingersoll-Ross (CIR) process where the boundary point zero is accessible. We consider numerical methods that have access to values of the driving Brownian motion $W$ at a finite number of time points. We show that the polynomial convergence rate of the $n$-th minimal errors for the class of adaptive algorithms as well as for the class of algorithms that rely on equidistant grids are equal to infinity and $1/2$, respectively. This shows that adaption results in a tremendously improved convergence rate. As a by-product, we obtain that the parameters appearing in the CIR process affect the convergence rate of strong approximation." @default.
- W2964129611 created "2019-07-30" @default.
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- W2964129611 date "2017-01-01" @default.
- W2964129611 modified "2023-09-24" @default.
- W2964129611 title "Optimal strong approximation of the one-dimensional squared Bessel process" @default.
- W2964129611 doi "https://doi.org/10.4310/cms.2017.v15.n8.a2" @default.
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