| Preface | p. ix |
| Notation | p. xi |
| General Notation | p. xi |
| Functions and Distributions | p. xiii |
| Measures and Integrals | p. xiv |
| Spaces of Functions, Measures and Distributions | p. xiv |
| Some Families of Functions | p. xvi |
| Norms, Scalar Products and Seminorms | p. xvii |
| Notation from Functional Analysis, Operators | p. xvii |
| Notations related to Pseudo-Differential Operators | p. xix |
| Notations related to Potential Theory and Harmonic Analysis | p. xix |
| Notation from Probability Theory | p. xx |
| Stochastic Processes and related Notations | p. xxi |
| Notations related to cadlag-Functions | p. xxii |
| Notations related to Hunt Processes and L[superscript p]-Markovian Semigroups | p. xxiii |
| Some more Special Notations | p. xxiii |
| Introduction: Pseudo-Differential Operators and Markov Processes | p. xxv |
| Markov Processes and Applications | p. 1 |
| Introduction | p. 3 |
| Essentials from Probability Theory | p. 9 |
| Some Remarks on [sigma]-Fields and Measures | p. 9 |
| Some Integration Theory | p. 17 |
| Measure and Topology | p. 22 |
| Independence | p. 24 |
| Conditional Expectation | p. 27 |
| Martingales and Stopping Times | p. 33 |
| Some Remarks to Stochastic Processes | p. 41 |
| Feller Processes | p. 45 |
| Projective Limits and Canonical Processes | p. 46 |
| Semigroups of Kernels, Transition Functions and Canonical Processes | p. 51 |
| A First Encounter with Sample Paths and Cadlag-Functions | p. 71 |
| Markov Processes and Feller Processes | p. 80 |
| The Shift Operator and the Strong Markov Property | p. 96 |
| The Martingale Problem for Feller Processes | p. 108 |
| Levy Processes and Translation Invariant Feller Semigroups | p. 115 |
| A Summary of Some Path Properties of Levy Processes | p. 141 |
| The Symbol of a Feller Process | p. 146 |
| Notes to Chapter 3 | p. 152 |
| The Martingale Problem | p. 157 |
| Probability Measures on D[subscript n] ([0, [infinity])) | p. 158 |
| Existence Results for the D[subscript n]-Martingale Problem | p. 174 |
| A Uniqueness Criterion for the Solvability of the Martingale Problem | p. 191 |
| A Localization Procedure | p. 198 |
| On the Well-Posedness of the Martingale Problem | p. 201 |
| The Martingale Problem and the Feller Property | p. 214 |
| Notes to Chapter 4 | p. 221 |
| L[superscript p]-sub-Markovian Semigroups and Hunt Processes | p. 223 |
| Why the Theory of Feller Processes is not Sufficient | p. 223 |
| Hunt Processes | p. 227 |
| Hunt Processes Associated with L[superscript p]-sub-Markovian Semigroups | p. 252 |
| Markov Processes Associated with an L[superscript p]-sub-Markovian Semigroup | p. 276 |
| Notes to Chapter 5 | p. 279 |
| Markov Processes and Potential Theory | p. 283 |
| Heuristic Links between Markov Processes and Potential Theory | p. 284 |
| Potential Theoretical Notions and their Probabilistic Counterparts | p. 287 |
| Potential Theory of Levy Processes and more Probabilistic Counterparts | p. 310 |
| Applications to Markov Processes | p. 319 |
| The Balayage-Dirichlet Problem | p. 329 |
| Notes to Chapter 6 | p. 351 |
| Selected Applications and Extensions | p. 353 |
| Fractional Derivatives as Generators of Markov Processes | p. 354 |
| Remarks on Markov Processes with State Spaces Having a Boundary | p. 368 |
| Making Parameters State Space Dependent | p. 385 |
| Remarks on Stochastic Spectral Analysis | p. 389 |
| Function Spaces Associated with a Continuous Negative Definite Function | p. 393 |
| Notes to Chapter 7 | p. 400 |
| Parametrix Construction for Evolution Equations | p. 403 |
| A Parameter Dependent Extension of Hoh's Calculus | p. 407 |
| On Roth's Method for Constructing Feller Semigroups | p. 411 |
| More Continuous Negative Definite Functions | p. 415 |
| More (Complete) Bernstein Functions | p. 419 |
| Corrections to Volume I | p. 422 |
| Corrections to Volume II | p. 423 |
| Changes in the Bibliography of Volume II | p. 424 |
| Bibliography | p. 425 |
| Author Index | p. 457 |
| Subject Index | p. 463 |
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