- Hacettepe Journal of Mathematics and Statistics
- Vol: 43 Issue: 6
- Approximation of some discrete-time stochastic processes by differential equations
Approximation of some discrete-time stochastic processes by differential equations
Authors : Raúl Fierro
Pages : 1035-1046
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Publication Date : 2014-12-01
Article Type : Research
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