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On the discretization schemes for the CIR (and Bessel squared) processes. (English) Zbl 1100.65007

The author considers the simulation of the Cox-Ingersoll-Ross (CIR) process defined by the stochastic integro-differential equation
\[ X_t=x_0+\int_0^t(a-kX_s)\, ds +\sigma\int_0^t\sqrt{X_s}\,dW_s,\quad t\in[0,T]. \] He presents several discretization schemes of both implicit and explicit types, studies their strong and weak convergence, examines them numerically, and compares then with already known schemes.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H20 Stochastic integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
45R05 Random integral equations
65R20 Numerical methods for integral equations
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