Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems

Laurent Gosse (1) , Olof Runborg (2)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 CSC

We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families. Moreover, we present a constructive algorithm to solve the moment problems numerically and prove that the algorithm computes the right solution.

Mots clés: Inverse problems; finite Markov moment problem; exponential transform.

Mots clés: exponential transform

Domaines: Analyse numérique [math.NA]; Applications [stat.AP]; Econométrie de la finance [q-fin.ST]

Laurent Gosse, Olof Runborg. Existence, uniqueness and a constructive solution algorithm for a class of finite Markov moment problems. SIAM Journal on Applied Mathematics, 2008, 68 (6), pp.1618-1640. ⟨10.1137/070692510⟩. ⟨hal-00323346⟩