Masatoshi Fukushima: Selecta (eBook)

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Niels Jacob, University of Wales Swansea, United Kingdom; Yoichi Oshima, Kumamoto University, Japan; Masayoshi Takeda, Tohoku University, Japan.

Preface 6
Curriculum vitae 8
Contents 10
Professor Masatoshi Fukushima – Scholar and Mentor 12
A construction of reflecting barrier Brownian motions for bounded domains 14
On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densities 47
Regular representations of Dirichlet spaces 83
Dirichlet spaces and strong Markov processes 102
On the generation of Markov processes by symmetric forms 142
Almost polar sets and ergodic theorem 176
On an LP-estimate of resolvents of Markov processes 192
Dirichlet spaces and additive functionals of finite energy 200
A note on irreducibility and ergodicity of symmetric Markov processes 207
Capacitary maximal inequalities and an ergodic theorem 215
Basic properties of Brownian motion and capacity on the Wiener space 222
A transformation of a symmetric Markov process and the Donsker-Varadhan theory 237
(r,p)-capacities for general Markov semigroups 253
On the continuity of plurisubharmonic functions along conformal diffusions 260
On Dirichlet forms for plurisubharmonic functions 267
On quasi-supports of smooth measures and closability of pre-Dirichlet forms 310
Dirichlet forms, diffusion processes and spectral dimensions for nested fractals 319
On a spectral analysis for the Sierpinski gasket 330
On a strict decomposition of additive functionals for symmetric diffusion processed 365
On a decomposition of additive functionals in the strict sense for a symmetric Markov process 370
Construction and decomposition of reflecting diffusions on Lipschitz domains with Hölder cusps 385
On semi-martingale characterizations of functions of symmetric Markov processes 422
On regular Dirichlet subspaces of H1(I) and associated linear diffusions 454
Entrance law, exit system and Lévy system of time changed processes 469
Extending Markov processes in weak duality by Poisson point processes of excursions 508
Acknowledgments 552
Bibliography 554