A problem of random choice and its deterministic structure

Abstract

A new problem of random choice for pills consumption process is formulated and considered. We find a kind of the Law of Large Numbers associated with any ordinary differential equation. This generalized LLN says that a stochastic analog of the Euler broken lines converges in probability to solution of the initial value problem for the ODE. This approach is applied to a stochastic process of pills consumption, and shows that after a suitable scaling the consumption process is almost deterministic, provided that the initial number of pills is large.