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VI: 18, 177-197, LNM 258 (1972)

**NAGASAWA, Masao**

Branching property of Markov processes (Markov processes)

To be completed

Keywords: Branching processes

Nature: Original

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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, 1011

Keywords: Boltzmann equation, Branching processes

Nature: Original

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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, 926

Keywords: Branching processes, Dirichlet problem

Nature: Original

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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 CourrĂ¨ge-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 theorem

Nature: Original

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XXVII: 01, 1-14, LNM 1557 (1993)

**NAGASAWA, Masao**

Principle of superposition and interference of diffusion processes

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XXXIV: 10, 257-288, LNM 1729 (2000)

**NAGASAWA, Masao**; **TANAKA, Hiroshi**

Time dependent subordination and Markov processes with jumps

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XXXV: 01, 1-27, LNM 1755 (2001)

**NAGASAWA, Masao**; **TANAKA, Hiroshi**

The principle of variation for relativistic quantum particles

Retrieve article from Numdam

Branching property of Markov processes (Markov processes)

To be completed

Keywords: Branching processes

Nature: Original

Retrieve article from Numdam

IX: 26, 471-485, LNM 465 (1975)

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, 1011

Keywords: Boltzmann equation, Branching processes

Nature: Original

Retrieve article from Numdam

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 (

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

Retrieve article from Numdam

X: 26, 532-535, LNM 511 (1976)

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 CourrĂ¨ge-Priouret,

Comment: The piecing out theorem is also reduced to a revival theorem in Meyer,

Keywords: Piecing-out theorem

Nature: Original

Retrieve article from Numdam

XXVII: 01, 1-14, LNM 1557 (1993)

Principle of superposition and interference of diffusion processes

Retrieve article from Numdam

XXXIV: 10, 257-288, LNM 1729 (2000)

Time dependent subordination and Markov processes with jumps

Retrieve article from Numdam

XXXV: 01, 1-27, LNM 1755 (2001)

The principle of variation for relativistic quantum particles

Retrieve article from Numdam