On a transformation of symmetric markov process and recurrence property

1987 ◽  
pp. 171-183 ◽  
Author(s):  
Yoichi Oshima ◽  
Masayoshi Takeda
Keyword(s):  
Markov Process ◽  
Recurrence Property ◽  
Symmetric Markov Process

scholarly journals On a fine capacity related to a symmetric Markov process

1972 ◽  
Vol 48 (8) ◽  
pp. 599-602 ◽  
Author(s):  
Masaru Takano
Keyword(s):  
Markov Process ◽  
Symmetric Markov Process

Diffusion processes with non-smooth diffusion coefficients and their density functions

1990 ◽  
Vol 115 (3-4) ◽  
pp. 231-242 ◽  
Author(s):  
T. J. Lyons ◽  
W. A. Zheng
Keyword(s):  
Markov Process ◽  
Elliptic Operator ◽  
Diffusion Coefficients ◽  
Dirichlet Process ◽  
Diffusion Processes ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Density Functions ◽  
Symmetric Markov Process ◽  
Image Position

SynopsisDenote by Xt an n-dimensional symmetric Markov process associated with an elliptic operatorwhere (aij) is a bounded measurable uniformly positive definite matrix-valued function of x. Let f(x, t) be a measurable function defined on Rn × [0, 1]. In this paper, we prove that f(Xt, t) is a regular Dirichlet process if and only if the following two conditions are satisfied:(i) For almost every and (ii) Let be a sequence of subdivisions of [0,1] so thatThenAs an application of the above result, we prove the following fact: Let p(y, t) be the probability density of the diffusion process Yt, associated with the elliptic operatorwhere (bi) are bounded measurable functions of x and we suppose that . Then, p(Yt, t) is a regular Dirichlet process and therefore p(.,.) satisfies (i) and (ii).

scholarly journals Teasing Apart Two Trees

2007 ◽  
Vol 16 (6) ◽  
pp. 903-922 ◽  
Author(s):  
M. A. STEEL ◽  
L. A. SZÉKELY
Keyword(s):  
Markov Process ◽  
Binary Sequences ◽  
Binary Trees ◽  
Sequence Length ◽  
Type Result ◽  
Model Tree ◽  
True Model ◽  
True Tree ◽  
Ramsey Type ◽  
Symmetric Markov Process

A widely studied model for generating binary sequences is to ‘evolve’ them on a tree according to a symmetric Markov process. We show that under this model distinguishing the true (model) tree from a false one is substantially ‘easier’ (in terms of the sequence length needed) than determining the true tree. The key tool is a new and near-tight Ramsey-type result for binary trees.

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