An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Ito, and H. P. McKean, among others. In this book, Ito discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a...
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion pro...
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface...
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating inte...
The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Levy's continuity theorem. This monograph focuses on this characteristic function approach and presents a renormalization theory called mod-ϕ convergence. This type of convergence is a relatively new concept with many deep ramifications, and has not previously been published in a single accessible volume. The authors construct an extremely flexible framework using this concept in order to study limit theorems and large deviations for a number of probabilistic models...
The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Levy's continuity theorem....
This is the only book discussing multifractal properties of densities of stable superprocesses, containing latest achievements while also giving the reader a comprehensive picture of the state of the art in this area. It is a self-contained presentation of regularity properties of stable superprocesses and proofs of main results and can serve as an introductory text for a graduate course. There are many heuristic explanations of technically involved results and proofs and the reader can get a clear intuitive picture behind the results and techniques.
This is the only book discussing multifractal properties of densities of stable superprocesses, containing latest achievements while also giving th...
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included.
This book is aimed at graduate students and researchers working in probability...
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages...
This book describes and characterizes an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggregate path coupling.
This book describes and characterizes an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggr...
