TY - JOUR
T1 - Diffusion processes on fractal fields
T2 - Heat kernel estimates and large deviations
AU - Hambly, B. M.
AU - Kumagai, T.
PY - 2003/11
Y1 - 2003/11
N2 - A fractal field is a collection of fractals with, in general, different Hausdorff dimensions, embedded in ℝ2. We will construct diffusion processes on such fields which behave as Brownian motion in ℝ2 outside the fractals and as the appropriate fractal diffusion within each fractal component of the field. We will discuss the properties of the diffusion process in the case where the fractal components tile ℝ2. By working in a suitable shortest path metric we will establish heat kernel bounds and large deviation estimates which determine the trajectories followed by the diffusion over short times.
AB - A fractal field is a collection of fractals with, in general, different Hausdorff dimensions, embedded in ℝ2. We will construct diffusion processes on such fields which behave as Brownian motion in ℝ2 outside the fractals and as the appropriate fractal diffusion within each fractal component of the field. We will discuss the properties of the diffusion process in the case where the fractal components tile ℝ2. By working in a suitable shortest path metric we will establish heat kernel bounds and large deviation estimates which determine the trajectories followed by the diffusion over short times.
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U2 - 10.1007/s00440-003-0284-0
DO - 10.1007/s00440-003-0284-0
M3 - Article
AN - SCOPUS:0344120288
SN - 0178-8051
VL - 127
SP - 305
EP - 352
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3
ER -