MATHEMATICS

Martingales in hyperfinite universum

E. A. Pchelintsev

Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: In article the approach to the theory of the martingales from positions of the non-standard analysis is considered. Definitions are entered and some important results of this theory with proofs are resulted, the part of the stated material belongs to the author. The applications of martingales are resulted in the theory of stochastic integration.

Keywords: Hyperfinite probability space, stochastic process, nonanticipating stochastic process, internal filtration, martingale, stochastic integral.

UDC: 519.216.8


Accepted: May 25, 2009