We define weighted fractional Brownian sheets, which are a class of Gaussian
random fields with four parameters that include fractional Brownian sheets as
special cases, and we give some of their properties. We show that for certain
values of the parameters the weighted fractional Brownian sheets are obtained
as limits in law of occupation time fluctuations of a stochastic particle
model. In contrast with some known approximations of fractional Brownian sheets
which use a kernel in a Volterra type integral representation of fractional
Brownian motion with respect to ordinary Brownian motion, our approximation
does not make use of a kernel
