@article {IOPORT.06052992,
    author       = {Chigansky, Pavel and Klebaner, Fima C.},
    title        = {The Euler-Maruyama approximation for the absorption time of the CEV diffusion.},
    year         = {2012},
    journal      = {Discrete and Continuous Dynamical Systems. Series B},
    volume       = {17},
    number       = {5},
    issn         = {1531-3492},
    pages        = {1455-1471},
    publisher    = {American Institute of Mathematical Sciences, Springfield, MO},
    doi          = {10.3934/dcdsb.2012.17.1455},
    abstract     = {Let the following stochastic differential equation $$ X_t = x + \int_0^t \mu X_s ds + \int_0^t \sigma X_s^{p} d B_s, $$ where $x \in \mathbb{R}_{+}, \mu \geq 0, \sigma > 0$ and $ p \in [1/2,1)$. By $B_t$ we denote the Brownian motion defined on a filtered probability space $(\Omega, {\cal F}, ({\cal F}_t), \mathbb{P})$ satisfying the usual conditions. Consider now the continuous time process $X^{\delta}$ which satisfies the Euler-Maruyama recursion at the grid points $t_j$, $$ X^{\delta}_{t_j} = X^{\delta}_{t_{j-1}} + \mu (X^{\delta}_{t_{j-1}})^+ + \sigma (X^{\delta}_{t_{j-1}})^{+p} \xi_j \sqrt{\delta}, $$ where $\xi_j$ is a sequence of i.i.d $N(0,1)$ random variables. Furthermore, let $$ \tau_{l}(X) = \inf \{ t \geq 0: X_t = l \}, $$ which is the hitting time of the level $l \in \mathbb{R}$. The main result of this paper is the following result: For any $\beta \in (0, \frac{1/2}{1-p})$, $$ \tau_{\delta^{\beta}} (X^{\delta}) \to \tau_0(X), \quad \text { as } \quad \delta \to 0, $$ where the convergence is in the weak sense.},
    reviewer     = {Nikolaos Halidias (Athens)},
    identifier   = {06052992},
}