Given the system is in equilibrium at time 0, we can compute the cumulative distribution function of the process maximum over a finite time horizon T in terms of Charlier polynomials.
orthogonal polynomials | Hermite polynomials | Macdonald polynomials | Jean-Michel Charlier | Chihara–Ismail polynomials | Carl Charlier | Brenke–Chihara polynomials | Wilson polynomials | Sister Celine's polynomials | Koornwinder polynomials | Joseph Charlier | Jacobi polynomials | Chihara-Ismail polynomials | Charlier polynomials | Charlier Cut | Boas–Buck polynomials | Angelescu polynomials | Al-Salam–Ismail polynomials |