Conjunction probability of smooth centered Gaussian processes

In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes and then we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic approximation by Euler characteristic method of Worsley and Friston and also implies the exact value of generalized Pickands constant in a special case. Some results for conjunction probability of correlated processes are also discussed.