VI: 18, 177-197, LNM 258 (1972)
NAGASAWA, Masao
Branching property of Markov processes (
Markov processes)
To be completed
Keywords: Branching processesNature: Original
Retrieve article from Numdam
IX: 26, 471-485, LNM 465 (1975)
NAGASAWA, Masao
Multiplicative excessive measures and duality between equations of Boltzmann and of branching processes (
Markov processes,
Statistical mechanics)
The author investigates the connection between the branching Markov processes constructed over some given Markov processes and a non-linear equation close to Boltzmann's equation. A special class of excessive measures for the branching Markov process is described and studied, as well as the corresponding dual processes
Comment: For other contributions by the same author devoted to the relation between branching process and non-linear equations, see
618,
1011Keywords: Boltzmann equation,
Branching processesNature: 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
X: 26, 532-535, LNM 511 (1976)
NAGASAWA, Masao
Note on pasting of two Markov processes (
Markov processes)
The pasting or piecing out theorem says roughly that two Markov processes taking values in two open sets and agreeing up to the first exit time of their intersection can be extended into a single Markov process taking values in their union. The word ``roughly'' replaces a precise definition, necessary in particular to handle jumps. Though the result is intuitively obvious, its proof is surprisingly messy. It is due to Courrège-Priouret,
Publ. Inst. Stat. Univ. Paris, 14, 1965. Here it is reduced to a ``revival theorem'' of Ikeda-Nagasawa-Watanabe,
J. Math. Kyoto Univ.,
8, 1968
Comment: The piecing out theorem is also reduced to a revival theorem in Meyer,
Ann. Inst. Fourier, 25,1975
Keywords: Piecing-out theoremNature: Original Retrieve article from Numdam
XXVII: 01, 1-14, LNM 1557 (1993)
NAGASAWA, Masao
Principle of superposition and interference of diffusion processes Retrieve article from Numdam
XXXIV: 10, 257-288, LNM 1729 (2000)
NAGASAWA, Masao;
TANAKA, Hiroshi
Time dependent subordination and Markov processes with jumps Retrieve article from Numdam
XXXV: 01, 1-27, LNM 1755 (2001)
NAGASAWA, Masao;
TANAKA, Hiroshi
The principle of variation for relativistic quantum particles Retrieve article from Numdam
