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Markov chain approximations for transition densities of Lévy processes


 
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1. Title Title of document Markov chain approximations for transition densities of Lévy processes
 
2. Creator Author's name, affiliation, country Aleksandar Mijatovic; Imperial College London; United Kingdom
 
2. Creator Author's name, affiliation, country Matija Vidmar; University of Warwick; United Kingdom
 
2. Creator Author's name, affiliation, country Saul Jacka; University of Warwick; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Levy process, continuous-time Markov chain, spectral representation, convergence rates for semi-groups and transition densities
 
3. Subject Subject classification 60G51
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Slovene Human Resources Development and Scholarship Fund
 
7. Date (YYYY-MM-DD) 2014-01-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2208
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2208
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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