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Let $X$ be a symmetric, pure jump, unimodal Levy process in $\mathbb{R}$ withan infinite Levy measure. We prove that for any fixed $t > 0$ the survivalprobability $P^x(\tau_{(-a,a)} > t)$ is nondecreasing on $(-a,0]$,nonincreasing on $[0,a)$ and concave on $(-a/2,a/2)$, where $a > 0$ and$\tau_{(-a,a)}$ is the first exit time of the process $X$ from $(-a,a)$. Wealso show a similar statement for sets $(-a,a) \times F \subset \mathbb{R}^d$.

Mid-concavity of survival probability for isotropic Levy processes