If this question has already been answered, please link me because I could not find anything online.
I have been using exponential Brownian motion in my models of stochastic population dynamics. The hitting times form a Levy distribution, which we cannot compute the expectation of. I am aware that the expectation of a Levy distribution diverges due to the heavy tails of the distribution, but how can I justify this analytically? We could set up the integral as $$\int xp(x)dx$$ but what exactly are we computing?
Thank you in advance for any insight!