Dirichlet forms associated with direct product diffusion processes

1982 ◽  
pp. 76-119 ◽  
Author(s):  
Matsuyo Tomisaki
Keyword(s):  
Direct Product ◽  
Diffusion Processes ◽  
Dirichlet Forms ◽  
Product Diffusion

Effective resistances for harmonic structures on p.c.f. self-similar sets

1994 ◽  
Vol 115 (2) ◽  
pp. 291-303 ◽  
Author(s):  
Jun Kigami
Keyword(s):  
Diffusion Processes ◽  
Difference Operator ◽  
Scaling Limit ◽  
Sierpinski Gasket ◽  
Dirichlet Forms ◽  
Sierpiński Gasket ◽  
Know How ◽  
Analysis On Fractals ◽  
Topological Description ◽  
Self Similar

In mathematics, analysis on fractals was originated by the works of Kusuoka [17] and Goldstein[8]. They constructed the ‘Brownian motion on the Sierpinski gasket’ as a scaling limit of random walks on the pre-gaskets. Since then, analytical structures such as diffusion processes, Laplacians and Dirichlet forms on self-similar sets have been studied from both probabilistic and analytical viewpoints by many authors, see [4], [20], [10], [22] and [7]. As far as finitely ramified fractals, represented by the Sierpinski gasket, are concerned, we now know how to construct analytical structures on them due to the results in [20], [18] and [11]. In particular, for the nested fractals introduced by Lindstrøm [20], one can study detailed features of analytical structures such as the spectral dimensions and various exponents of heat kernels by virtue of the strong symmetry of nested fractals, cf. [6] and [15]. Furthermore in [11], Kigami proposed a notion of post critically finite (p.c.f. for short) self-similar sets, which was a pure topological description of finitely ramified self-similar sets. Also it was shown that we can construct Dirichlet forms and Laplacians on a p.c.f. self-similar set if there exists a difference operator that is invariant under a kind of renormalization. This invariant difference operator was called a harmonic structure. In Section 2, we will give a review of the results in [11].

scholarly journals Perturbations of functional inequalities for Lévy type Dirichlet forms

2015 ◽  
Vol 27 (6) ◽  
Author(s):  
Xin Chen ◽  
Feng-Yu Wang ◽  
Jian Wang
Keyword(s):  
Diffusion Processes ◽  
Dirichlet Forms ◽  
Functional Inequalities ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Natural Extensions ◽  
Infinite Range

AbstractPerturbations of super Poincaré and weak Poincaré inequalities for Lévy type Dirichlet forms are studied. When the range of jumps is finite, our results are natural extensions to the corresponding ones derived earlier for diffusion processes; and we show that the study for the situation with infinite range of jumps is essentially different. Some examples are presented to illustrate the optimality of our results.

Convergence of Time Changed Skew Product Diffusion Processes

2011 ◽  
Vol 38 (1) ◽  
pp. 31-55 ◽  
Author(s):  
Tomoko Takemura
Keyword(s):  
Diffusion Processes ◽  
Skew Product ◽  
Product Diffusion

scholarly journals Agent-Based Simulation of Product Diffusion with Network Externality in a Heterogeneous Consumer Network

2011 ◽  
Vol 15 (2) ◽  
pp. 173-179 ◽  
Author(s):  
Nobutada Fujii ◽  
◽  
Toshiya Kaihara ◽  
Takashi Eda ◽  
Keyword(s):  
Complex Networks ◽  
Multiagent Systems ◽  
Diffusion Processes ◽  
Product Market ◽  
Network Externality ◽  
Threshold Models ◽  
Product Diffusion ◽  
Consumer Heterogeneity ◽  
Agent Based ◽  
Simulation Results

In a product market with network externality, outperforming products are not always disseminated. Product markets are often modeled and examined by simulation to clarify product diffusion processes. In earlier work, where multiagent systems and complex networks were used to model the product market, consumer heterogeneity was not considered despite its influence on the product diffusion process. This paper introduces threshold models into multiagent-systembased simulation in complex networks to realize consumer heterogeneity. The feasibility of the proposed method is discussed using computer simulation results, and consumer heterogeneity and network structure affect product diffusion processes.

DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS II: CLOSABILITY AND DIFFUSION PROCESSES

1989 ◽  
Vol 01 (02n03) ◽  
pp. 313-323 ◽  
Author(s):  
S. ALBEVERIO ◽  
T. HIDA ◽  
J. POTTHOFF ◽  
M. RÖCKNER ◽  
L. STREIT
Keyword(s):  
White Noise ◽  
Diffusion Processes ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
White Noise Analysis ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Dimensional Diffusion ◽  
White Noise Functionals ◽  
And Diffusion

It is shown that infinite dimensional Dirichlet forms as previously constructed in terms of (generalized) white noise functionals fit into the general framework of classical Dirichlet forms on topological vector spaces. This entails that all results obtained there are applicable. Admissible functionals give rise to infinite dimensional diffusion processes.

DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS II: CLOSABILITY AND DIFFUSION PROCESSES

2001 ◽  
pp. 364-374 ◽  
Author(s):  
S. ALBEVERIO ◽  
T. HIDA ◽  
J. POTTHOFF ◽  
M. RÖCKNER ◽  
L. STREIT
Keyword(s):  
White Noise ◽  
Diffusion Processes ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
White Noise Analysis ◽  
And Diffusion

scholarly journals Averaging principle for diffusion processes via Dirichlet forms

2014 ◽  
Vol 41 (4) ◽  
pp. 1033-1063 ◽  
Author(s):  
Florent Barret ◽  
Max von Renesse
Keyword(s):  
Diffusion Processes ◽  
Dirichlet Forms ◽  
Averaging Principle
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