In recent years, there has been an increasing interest in 
opinion dynamics in social networks. The present paper 
proposes an attempt to develop a computational framework
for such dynamics in continuous time with an additive 
noise representing self-beliefs. We derive a partial 
differential equation for the distribution of opinions 
differences. The main point is that there is a calculus 
based on Mellin transforms that allows one to solve this 
type of equations in closed form.

The main new result of this approach is a closed form solution
for the bounded confidence model within this stochastic continuous
time framework. This is done here in the simplest possible 
cases (small number of agents, present of stubborn agents, 
one dimensional opinions).