## Masatoshi Fukushima: SelectaMasatoshi Fukushima is one of the most influential probabilists of our times. His fundamental work on Dirichlet forms and Markov processes made Hilbert space methods a tool in stochastic analysis and by this he opened the way to several new developments. His impact on a new generation of probabilists can hardly be overstated. These Selecta collect 25 of Fukushima's seminal articles published between 1967 and 2007. |

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### Contents

R5 3 | 36 |

Regular representations of Dirichlet spaces R8 | 72 |

Dirichlet spaces and strong Markov processes R9 | 91 |

On a strict decomposition of additive functionals for symmetric diffusion | 354 |

Construction and decomposition of reflecting diffusions on Lipschitz domains | 374 |

On semimartingale characterizations of functions of symmetric Markov | 411 |

On regular Dirichlet subspaces of HlI and associated linear diffusions | 443 |

Entrance law exit system and Levy system of time changed processes | 458 |

Extending Markov processes in weak duality by Poisson point processes | 497 |

Acknowledgments | 541 |

545 | |

### Common terms and phrases

absolutely continuous additive functional admits AF's associated assume Borel measure Borel set boundary bounded variation Brownian motion cadlag continuous function converges D-space decomposition defined denote dense diffusion process domain duality with respect equation equivalent excursions exhaustive sequence exists Feller measures finely open sets finite Fukushima G E0 Ga(x hand side Hence holds Hunt process identity implies inequality Lebesgue measure Lemma Levy system Markov process Markov property Math nearly Borel nest non-negative open set PCAF Poisson point process positive constant proof of Theorem properly exceptional set Proposition q.e. finely quasi-continuous quasi-regular Dirichlet space Radon measure regular Dirichlet space regular representation resolvent density resp Revuz measure right process sample path satisfying condition semimartingale signed measure smooth measure strict sense strongly regular subset symmetric Theorem Theorem 3.1 unique weak duality zero capacity