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Path-Valued Processes and Stochastic Flows
In this chapter, we study a class of stochastic flows by means of stochastic equations and measure-valued processes. They are reformulations of the...
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State-Dependent Immigration Structures
In this chapter we give the construction of a class of Dawson–Watanabe superprocesses with state-dependent immigration. The basic idea is to...
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Martingale Problems of Superprocesses
Martingale problems play a very important role in the study of Markov processes. In this chapter we investigate some martingale problems associated...
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Basic Regularities of Superprocesses
In this chapter we prove some basic regularities of Dawson–Watanabe superprocesses. The theory is developed here in the Borel right setting, which is...
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Structures of Independent Immigration
In this chapter we study independent immigration structures associated with MBprocesses. We first give a formulation of the structures using skew...
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Generalized Ornstein–Uhlenbeck Processes
Generalized Ornstein–Uhlenbeck processes constitute a large class of explicit examples of Markov processes in infinite-dimensional spaces with rich...
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Dyson’s Model in Infinite Dimensions Is Irreducible
Dyson’s model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of...
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Scattering Lengths for Additive Functionals and Their Semi-classical Asymptotics
Scattering lengths for positive additive functionals of symmetric Markov processes are studied. The additive functionals considered here are not...
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Interactions Between Trees and Loops, and Their Representation in Fock Space
It has been observed that on a weighted graph, an extension of Wilson’s algorithm provides an independent pair...
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Hölder Estimates for Resolvents of Time-Changed Brownian Motions
In this paper, we study time changes of Brownian motions by positive continuous additive functionals. Under a certain regularity condition on the...
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On Singularity of Energy Measures for Symmetric Diffusions with Full Off-Diagonal Heat Kernel Estimates II: Some Borderline Examples
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpiński gaskets and each of which is equipped...
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Infinite Particle Systems with Hard-Core and Long-Range Interaction
A system of Brownian hard balls is regarded as a reflecting Brownian motion in the configuration space and can be represented by a solution to a...
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Hermitizable, Isospectral Matrices or Differential Operators
This paper reports the study on Hermitizable problem for complex matrix or second order differential operator. That is the existence and construction...
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Random Riemannian Geometry in 4 Dimensions
We construct and analyze conformally invariant random fields on 4-dimensional Riemannian manifolds (M, g). These centered Gaussian fields h, called...
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Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results
This article gives an overview of some recent progress in the study of sharp two-sided estimates for the transition density of a large class of...
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Maximal Displacement of Branching Symmetric Stable Processes
We determine the limiting distribution and the explicit tail behavior for the maximal displacement of a branching symmetric stable process with...
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On Non-negative Solutions to Space-Time Partial Differential Equations of Higher Order
We discuss when certain higher order partial differential operators in space and time admit non-negative solutions which have a semigroup...
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Equivalence of the Strong Feller Properties of Analytic Semigroups and Associated Resolvents
In this paper, we give sufficient conditions for the equivalence between semigroup strong Feller property and resolvent strong Feller property.
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The Dynamics of a Volterra Cubic Operator
In this paper, we consider a family of Volterra cubic stochastic operators defined on the two-dimensional simplex depending on two parameters. It is...
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Block Markov Chains on Trees
We introduce a new class of tree-indexed Markov processes, so-called block Markov chains (BMCs). We clarify the structure of BMCs in connection with...