Properties of Strong Local Nondeterminism and Local Times of Stable Random Fields

2011 ◽  
pp. 279-308 ◽  
Author(s):  
Yimin Xiao
Keyword(s):  
Random Fields ◽  
Local Times ◽  
Stable Random Fields ◽  
Local Nondeterminism

scholarly journals Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

2008 ◽  
Vol 40 (02) ◽  
pp. 529-547
Author(s):  
Francisco J. Piera ◽  
Ravi R. Mazumdar ◽  
Fabrice M. Guillemin
Keyword(s):  
Random Fields ◽  
Diffusion Coefficients ◽  
Boundary Behavior ◽  
Stationary Regime ◽  
Product Form ◽  
Local Times ◽  
Nonnegative Orthant ◽  
State Dependent ◽  
The Times ◽  
And Diffusion

In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of ℝ n . We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary regime to the case when the drift and diffusion coefficients, as well as the directions of reflection, are random fields over space.

scholarly journals Operator scaling stable random fields

2007 ◽  
Vol 117 (3) ◽  
pp. 312-332 ◽  
Author(s):  
Hermine Biermé ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Fields ◽  
Stable Random Fields

scholarly journals Extrapolation of stable random fields

2013 ◽  
Vol 115 ◽  
pp. 516-536 ◽  
Author(s):  
Wolfgang Karcher ◽  
Elena Shmileva ◽  
Evgeny Spodarev
Keyword(s):  
Random Fields ◽  
Stable Random Fields
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