Bernstein processes described by forward and backward heat equations

Mohamad Houda (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We present some results on Bernstein processes which are Brownian diffusions that appear in Euclidean Quantum Mechanics: We express the distributions of these processes with the help of those of Bessel processes. We then determine two solutions of the dual equation of the heat equation with potential. This continues the calculation of Lescot for the solution with an Ornstein-Uhlenbek process .

Mots clés: Bessel processes; Bernstein processes; interest rate models

Domaines: Probabilités [math.PR]

Mohamad Houda. Bernstein processes described by forward and backward heat equations. 2013. ⟨hal-00864437⟩