  In this paper, we study the classical Keller - Segel system on a
two-dimensional domain perturbed by a pair of Wiener processes, where the
leading diffusion term is replaced by a porous media term. Since the randomness
is intrinsic, the interpretation of the stochastic integral in the Stratonovich
sense is natural. We construct a solution (integral) operator and establish its
continuity and compactness properties in an appropriately chosen Banach space.
In this manner, we formulate a stochastic version of the Schauder - Tychonoff
Type Fixed Point Theorem which is specific to our problem to obtain a solution.
In-kind, we achieve the existence of a martingale solution.
