symbol $\mathcal{M}^{+}_{\alpha,\beta}$ is used for Pucci’s maximal operator, defined on a $d \times d$ matrices $B$ by $$\mathcal{M}^{+}_{\alpha,\beta}(B)=\sup_{\alpha I \leq A \leq \beta I} A:B,$$ where the supremum is taken over all $d\times d$ matrices $A$ with eigenvalues between $\alpha$ and $\beta$. The symbol $\mathcal{P}$ denotes the predictable sigma algebra on $\Omega \times [0,T]$ generated by the Brownian motion $W$. For a function $\rho$ depending on both time $t$ and other variables, we often write $\rho_{t}$ to denote evaluation at time $t$ (not to be confused with differentiation in $t$). We also use the notation $A \leqs B$ provided there exists a universal constant $C$ such that $A \leq C B$.

Structure of the article
------------------------

The article is structured as follows. In Section \[sec:KES\], we introduce the kinetic formulation of the SPDE \[eq:SPDE\]. Section \[subsec:aprioribds\] sketches the formal a priori estimate at the heart of the main result, Theorem \[thm:MainResult\]. In Section \[sec:exist\] we define generalized kinetic solutions and prove their existence. In Section \[sec:unique\], we give conditions for a generalized kinetic solution to be a kinetic solution and use this to complete the proof of Theorem \[thm:MainResult\].

Kinetic entropy solutions {#sec:KES}
-------------------------

Let us now give our precise 