  We show that the derivative of the intersection and self-intersection local
times of alpha-stable processes are exponentially integrable for certain
parameter values. This includes the Brownian motion case. We also discuss
related results present in the literature for fractional Brownian motion, and
in particular give a counter-example to a result in [Guo, J., Hu, Y., and Xiao,
Y., Higher-order derivative of intersection local time for two independent
fractional Brownian motions, Journal of Theoretical Probability 32, (2019), pp.
1190-1201] related to this question.
