Approximation of some discrete-time stochastic processes by differential equations

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

Raúl Fierro

https://izlik.org/JA85XM63XD

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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