Description

Book Synopsis
In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including $n$-dimensional cube $[0, 1]^n$ are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows.

Table of Contents
  • Introduction
  • Generalized Sierpinski carpets
  • Standing assumptions and notations
  • Gauge function
  • The Brownian motion and the Green function
  • Time change of the Brownian motion
  • Scaling of the Green function
  • Resolvents
  • Poincare inequality
  • Heat kernel, existence and continuity
  • Measures having weak exponential decay
  • Protodistance and diagonal lower estimate of heat kernel
  • Proof of Theorem 1.1
  • Random measures having weak exponential decay
  • Volume doubling measure and sub-Gaussian heat kernel estimate
  • Examples
  • Construction of metrics from gauge function
  • Metrics and quasimetrics
  • Protodistance and the volume doubling property
  • Upper estimate of $p_\mu (t, x, y)$
  • Lower estimate of $p_\mu (t, x, y)$
  • Non existence of super-Gaussian heat kernel behavior
  • Bibliography
  • List of notations
  • Index

    Time Changes of the Brownian Motion Poincare

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      A Paperback by Jun Kigami

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        Publisher: MP-AMM American Mathematical
        Publication Date: 7/30/2019 12:00:00 AM
        ISBN13: 9781470436209, 978-1470436209
        ISBN10: 1470436205

        Description

        Book Synopsis
        In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including $n$-dimensional cube $[0, 1]^n$ are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows.

        Table of Contents
        • Introduction
        • Generalized Sierpinski carpets
        • Standing assumptions and notations
        • Gauge function
        • The Brownian motion and the Green function
        • Time change of the Brownian motion
        • Scaling of the Green function
        • Resolvents
        • Poincare inequality
        • Heat kernel, existence and continuity
        • Measures having weak exponential decay
        • Protodistance and diagonal lower estimate of heat kernel
        • Proof of Theorem 1.1
        • Random measures having weak exponential decay
        • Volume doubling measure and sub-Gaussian heat kernel estimate
        • Examples
        • Construction of metrics from gauge function
        • Metrics and quasimetrics
        • Protodistance and the volume doubling property
        • Upper estimate of $p_\mu (t, x, y)$
        • Lower estimate of $p_\mu (t, x, y)$
        • Non existence of super-Gaussian heat kernel behavior
        • Bibliography
        • List of notations
        • Index

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