| Abstract: |
| For Gaussian random fields with values in $\R^d$, sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in particular to the solutions of systems of linear SPDEs. For non-Gaussian random fields, the available bounds are less sharp. For systems of stochastic heat equations, a sharp lower bound was obtained in [R.C. Dalang and F. Pu, Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k \geq 1. Electron. J. Probab. 25 (2020), Paper No. 40, 31 pp]. Here, we obtain the corresponding sharp upper bound. |
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