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August  2014, 19(6): 1549-1562. doi: 10.3934/dcdsb.2014.19.1549

## On strong causal binomial approximation for stochastic processes

 1 Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, Western Australia, 6845

Received  November 2013 Revised  March 2014 Published  June 2014

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. Moreover, this approximation can be causal, i.e., at every time it requires only past historical values of the underlying process. In addition, possibility of approximation of solutions of stochastic differential equations by solutions of ordinary equations with binary noise is established. Some consequences for the financial modelling and options pricing models are discussed.
Citation: Nikolai Dokuchaev. On strong causal binomial approximation for stochastic processes. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1549-1562. doi: 10.3934/dcdsb.2014.19.1549
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