On the convergence of discrete processes with multiple independent variables

Naoyuki Ishimura, Naohiro Yoshida

Abstract


We discuss discrete stochastic processes with two independent variables: one is the standard symmetric random walk, and the other is the Poisson process. Convergence of discrete stochastic processes is analysed, such that the symmetric random walk tends to the standard Brownian motion. We show that a discrete analogue of Ito’s formula converges to the corresponding continuous formula.


doi:10.1017/S1446181116000389

Keywords


discrete processes, convergence, Ito’s formula.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11089



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.