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

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In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form cases K₍ₓ,ₜ₎(D u)uₜ (x,t)= 12 <D² u J₍ₓ,ₜ₎(D u),J₍ₓ,ₜ₎(D u) (x,t) &in Ωₜ, u(x,t)=F(x)&onΓ, cases where Ωₜ=Ω×(0,T] and Γ is its parabolic boundary. This problem can be viewed as a version with spatial and time dependence of the evolution problem given by the infinity Laplacian, uₜ (x,t)= <D² u (x,t) D u/|Du| (x,t), D u/|Du| (x,t)>.