| Preface | 7 |
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| 1 Dirichlet forms | 11 |
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| 1.1 Semi-Dirichlet forms and resolvents | 11 |
| 1.2 Closability and regular Dirichlet forms | 19 |
| 1.3 Transience and recurrence of Dirichlet forms | 22 |
| 1.4 An auxiliary bilinear form | 30 |
| 1.5 Examples | 40 |
| 1.5.1 Diffusion case | 40 |
| 1.5.2 Jump type case | 46 |
| 2 Some analytic properties of Dirichlet forms | 53 |
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| 2.1 Capacity | 53 |
| 2.2 Quasi-Continuity | 61 |
| 2.3 Potential of measures | 65 |
| 2.4 An orthogonal decomposition of the Dirichlet forms | 70 |
| 3 Markov processes | 82 |
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| 3.1 Hunt processes | 82 |
| 3.2 Excessive functions and negligible sets | 86 |
| 3.3 Hunt processes associated with a regular Dirichlet form | 90 |
| 3.4 Negligible sets for Hunt processes | 99 |
| 3.5 Decompositions of Dirichlet forms | 104 |
| 4 Additive functionals and smooth measures | 122 |
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| 4.1 Positive continuous additive functionals | 122 |
| 4.2 Dual PCAFs and duality relations | 138 |
| 4.3 Time changes and killings | 148 |
| 5 Martingale AFs and AFs of zero energy | 159 |
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| 5.1 Fukushima’s decomposition of AFs | 159 |
| 5.1.1 AFs generated by functions of F | 161 |
| 5.1.2 Martingale additive functionals of finite energy | 162 |
| 5.1.3 CAFs of zero energy | 164 |
| 5.2 Beurling-Deny type decomposition | 179 |
| 5.3 CAFs of locally zero energy in the weak sense | 189 |
| 5.4 Martingale AFs of strongly local Dirichlet forms | 200 |
| 5.5 Transformations by multiplicative functionals | 213 |
| 5.6 Conservativeness and recurrence of Dirichlet forms | 218 |
| 6 Time dependent Dirichlet forms | 225 |
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| 6.1 Time dependent Dirichlet forms and associated resolvents | 225 |
| 6.2 A parabolic potential theory | 234 |
| 6.3 Associated space-time processes | 249 |
| 6.4 Additive functionals and associated measures | 258 |
| 6.5 Some stochastic calculus | 269 |
| Notes | 277 |
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| Bibliography | 282 |
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| Index | 293 |
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