Approximation of some discrete-time stochastic processes by differential equations

Year 2014, Volume: 43 Issue: 6, 1035 - 1046, 01.12.2014

Raúl Fierro

Abstract

This work deals with solutions of ordinary differential equations as
approximations of some discrete-time stochastic processes. Similarly,
these stochastic processes may be seen as schemes of approximation for
this solution. Indeed, these stochastic schemes are defined and their
convergence to the solution of a differential equation is proven. Moreover, the asymptotic distribution of the fluctuations about the limit
solution is studied. This fact gives the asymptotic distribution of a
random global error of approximation. Main results are illustrated by
means of the so called SIS epidemic model and numerical simulations
are carried out.

Keywords

Law of Large Numbers, Central Limit Theorem, Numerical schemes, SIS epidemic model

References

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