III: 03, 34-92, LNM 88 (1969)
CAIROLI, Renzo
Étude probabiliste d'un problème de Dirichlet (
Several parameter processes)
This paper aims at a better understanding of separately harmonic functions with respect to a product of two Markov processes, which provide one of the main examples of two parameter martingales (the other one being the Brownian sheet). Here the recently published work of J.~Walsh (
Ann. Inst. Fourier, 18, 1968) on the Dirichlet problem for biharmonic functions was discussed and reinterpreted
Comment: An early step in the theory of two parameter martingales. See also Cairoli,
Publ. Inst. Stat. Univ. Paris, 15, 1966
Keywords: Dirichlet problem,
Biharmonic functionsNature: Original
Retrieve article from Numdam
X: 11, 184-193, LNM 511 (1976)
NAGASAWA, Masao
A probabilistic approach to non-linear Dirichlet problem (
Markov processes)
The theory of branching Markov processes in continuous time developed in particular by Ikeda-Nagasawa-Watanabe (
J. Math. Kyoto Univ.,
8, 1968 and
9, 1969) and Nagasawa (
Kodai Math. Sem. Rep. 20, 1968) leads to the probabilistic solution of a non-linear Dirichlet problem
Comment: For other contributions by the same author devoted to the relation between branching process and non-linear equations, see
618,
926Keywords: Branching processes,
Dirichlet problemNature: Original Retrieve article from Numdam
