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We consider the fractional stochastic heat equation on the $d$-dimensionaltorus $\mathbb{T}^d:=[-1,1]^d$, $d\geq 1$, with periodic boundary conditions:$$ \partial_t u(t,x)=-(-\Delta)^{\alpha/2}u(t,x)+\sigma(t,x,u)\dot{F}(t,x)\quad x\in\mathbb{T}^d,t\in\mathbb{R}^+ ,$$ where $\alpha\in(1,2]$ and $\dot{F}(t,x)$ isa white in time and colored in space noise. We assume that $\sigma$ isLipschitz in $u$ and uniformly bounded. We provide small ball probabilities forthe solution $u$ when $u(0,x)\equiv 0$.

Small ball probabilities for the fractional stochastic heat equation driven by a colored noise