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Time Changes of the Brownian Motion.
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. In case of the Brownian motion on [0, 1]^n, density of the medium...
| Call Number: | Libro Electrónico |
|---|---|
| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence :
American Mathematical Society,
2019.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1250. |
| Subjects: | |
| Online Access: | Texto completo |
Table of Contents:
- Cover; Title page; Chapter 1. Introduction; Chapter 2. Generalized Sierpinski carpets; Chapter 3. Standing assumptions and notations; Chapter 4. Gauge function; Chapter 5. The Brownian motion and the Green function; Chapter 6. Time change of the Brownian motion; Chapter 7. Scaling of the Green function; Chapter 8. Resolvents; Chapter 9. Poincaré inequality; Chapter 10. Heat kernel, existence and continuity; Chapter 11. Measures having weak exponential decay; Chapter 12. Protodistance and diagonal lower estimateof heat kernel; Chapter 13. Proof of Theorem 1.1
- Chapter 14. Random measures having weak exponential decayChapter 15. Volume doubling measure and sub-Gaussian heat kernel estimate; Chapter 16. Examples; Chapter 17. Construction of metrics from gauge function; Chapter 18. Metrics and quasimetrics; Chapter 19. Protodistance and the volume doubling property; Chapter 20. Upper estimate of _{ }(,); Chapter 21. Lower estimate of _{ }(,); Chapter 22. Non existence of super-Gaussian heat kernel behavior; Bibliography; List of Notations; Index; Back Cover