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In this paper we use probabilistic arguments (Tug-of-War games) to obtainexistence of viscosity solutions to a parabolic problem of the form $$ {cases}K_{(x,t)}(D u)u_t (x,t)= \frac12 <D^2 u J_{(x,t)}(D u),J_{(x,t)}(D u) (x,t)&{in} \Omega_T, u(x,t)=F(x)&{on}\Gamma, {cases} $$ where$\Omega_T=\Omega\times(0,T]$ and $\Gamma$ is its parabolic boundary. Thisproblem can be viewed as a version with spatial and time dependence of theevolution problem given by the infinity Laplacian, $ u_t (x,t)= <D^2 u (x,t)\frac{D u}{|Du|} (x,t),\, \frac{D u}{|Du|} (x,t)>$.

Tug-of-War games and parabolic problems with spatial and time dependence