In the paper we consider the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields. In particular, we provide closed-form asymptotic bounds for the density functions and, under smoothness conditions, we derive exact tail approximations of the density functions.
"On the density functions of integrals of Gaussian random fields." Adv. in Appl. Probab. 45 (2) 398 - 424, June 2013. https://doi.org/10.1239/aap/1370870124