An estimation problem for the intensity density of Poisson processes

A Poisson process $X_\varepsilon(t)$ with the intensity density function $\varepsilon^{-1}\lambda(t)$ is observed on an interval $[a,b]$. The problem is to estimate the function $\lambda(t)$. It is known that the unknown function $\lambda(t)$ belongs to a given class of functions analytic in a given region $G\supset[a,b]$ and is bounded there by a given constant $M$. The parameter $\varepsilon$ is supposed to be known and we consider the problem as $\varepsilon\to0$.