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III: 03, 34-92, LNM 88 (1969)
√Čtude probabiliste d'un probl√®me 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 functions
Nature: Original
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X: 11, 184-193, LNM 511 (1976)
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, 926
Keywords: Branching processes, Dirichlet problem
Nature: Original
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