@Article{Mishura2015,
author = "Mishura, Yuliya",
title = "Diffusion approximation of recurrent schemes for financial markets, with application to the Ornstein-Uhlenbeck process",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "1",
pages = "99--116",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.1.99",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.1.99",
abstract = "We adapt the general conditions of the weak convergence for the sequence of processes with discrete time to the diffusion process towards the weak convergence for the discrete-time models of a financial market to the continuous-time diffusion model. These results generalize a classical scheme of the weak convergence for discrete-time markets to the Black-Scholes model. We give an explicit and direct method of approximation by a recurrent scheme. As an example, an Ornstein-Uhlenbeck process is considered as a limit model.",
keywords = "diffusion approximation, semimartingale, recurrent scheme, financial market, multiplicative scheme, Ornstein-Uhlenbeck process",
issn = "1232-9274"
}