Intro
Preface
List of Masatoshi Fukushima's Publications
Contents
Markov Uniqueness and Fokker-Planck-Kolmogorov Equations
1 Introduction and Framework
2 The Main Idea and a Parabolic Condition for Uniqueness
3 Some Uniqueness Results for FPKEs
3.1 Fokker-Planck-Kolmogorov Equations
3.2 Nondegenerate VMO Diffusion Coefficients
3.3 Nondegenerate Locally Lipschitz Diffusion Coefficients
3.4 Nondegenerate Diffusion Coefficients and the Lyapunov Function Condition
3.5 Degenerate Diffusion Coefficients
4 Applications to the Markov Uniqueness Problem

4.1 The Framework
4.2 Nondegenerate VMO Diffusion Coefficients
4.3 Nondegenerate Locally Lipschitz Diffusion Coefficients
4.4 Nondegenerate Diffusion Coefficients and Lyapunov Function Conditions
4.5 Degenerate Diffusion Coefficients
References
A Chip-Firing and a Riemann-Roch Theorem on an Ultrametric Space
1 Introduction
2 Laplacian and Riemann-Roch Theorem on Ultrametric Space with Finite Vertices
3 Unification of Ultrametric Space with Finite Verteces
4 Riemann-Roch Theorem on Ultrametric Space with Countably Many Vertices
References

Hermitizable, Isospectral Matrices or Differential Operators
1 Hermitizable, Isospectral Matrices
2 Hermitizable, Isospectral Differential Operators
References
On Strongly Continuous Markovian Semigroups
References
Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results
1 Introduction
2 Stability of Heat Kernel Estimates for Symmetric Diffusions with Jumps
2.1 Two-Sided Heat Kernel Estimates
2.2 Example
3 Symmetric Reflected Diffusions with Jumps in Inner Uniform Domains
3.1 Reflected Diffusions on Inner Uniform Domains

3 Some Translation Invariant Pseudo-differential Operators
4 Some Discussions on the Case upper N equals 2N=2
5 Higher Order Partial Differential Equations Admitting Non-negative Solutions
References
Monotonicity Properties of Regenerative Sets and Lorden's Inequality
1 Introduction
2 Lorden's Inequality
3 Monotone Potential Density
4 Concluding Remarks
References
Doob Decomposition, Dirichlet Processes, and Entropies on Wiener Space
1 Introduction
2 Doob Decomposition in Continuous Time
3 Entropies and Couplings on Wiener Space
References