| Título: | Markov chain approximations for transition densities of Lévy processes |
| Autores: |
Mijatovic, Aleksandar; Imperial College London Vidmar, Matija; University of Warwick Jacka, Saul; University of Warwick |
| Fecha: | 2014-01-02 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Levy process, continuous-time Markov chain, spectral representation, convergence rates for semi-groups and transition densities 60G51 |
| Descripción: | We consider the convergence of a continuous-time Markov chain approximation $X^h$, $h>0$, to an $\mathbb{R}^d$-valued Lévy process $X$. The state space of $X^h$ is an equidistant lattice and its $Q$-matrix is chosen to approximate the generator of $X$. In dimension one ($d=1$), and then under a general sufficient condition for the existence of transition densities of $X$, we establish sharp convergence rates of the normalised probability mass function of $X^h$ to the probability density function of $X$. In higher dimensions ($d>1$), rates of convergence are obtained under a technical condition, which is satisfied when the diffusion matrix is non-degenerate. |
| Idioma: | Inglés |
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