Fast -approximation of integral-type functionals of Markov processes
Volume 2, Issue 2 (2015), pp. 165–171
Pub. online: 28 July 2015
Type: Research Article
Open Access
Open Access
Received
8 July 2015
8 July 2015
Revised
20 July 2015
20 July 2015
Accepted
22 July 2015
22 July 2015
Published
28 July 2015
28 July 2015
Abstract
In this paper, we provide strong $L_{2}$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its transition probability density, we get the accuracy that coincides with that obtained in [3] for a one-dimensional diffusion process.
References
Ganychenko, I., Kulik, A.: Rates of approximation of nonsmooth integral-type functionals of Markov processes. Mod. Stoch., Theory Appl. 2, 117–126 (2014) MR3316480. doi:10.15559/vmsta-2014.12
Kohatsu-Higa, A., Makhlouf, A., Ngo, H.L.: Approximations of non-smooth integral type functionals of one dimensional diffusion precesses. Stoch. Process. Appl. 124, 1881–1909 (2014) MR3170228. doi:10.1016/j.spa.2014.01.003
Sznitman, A.: Brownian Motion, Obstacles and Random Media. Springer, Berlin (1998) MR1717054. doi:10.1007/978-3-662-11281-6
