On the estimation of the intensity density function of Poisson random field outside of the observation region

A Poisson random field with the intensity density function $\frac{\lambda(x)}\varepsilon$ is observed in a bounded region $G\subseteq\mathbb R^d$. It is supposed that the unknown function $\lambda$ belongs to a known class of entire functions. The parameter $\varepsilon$ is supposed to be known. The problem is to estimate the value $\lambda(x)$ at the points $x\notin G$. We consider an asymptotic setup of the problem when $\varepsilon\to0$.