Semimartingale decomposition and heat kernel estimates of reflected stable-like processes with variable order
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 526-551
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We investigate symmetric reflected stable-like processes on a compact set $
\overline{E} \subset \mathbf{R}^d$ associated to nonlocal Dirichlet forms with
variable order $\alpha{(\,\cdot\,,\cdot\,)}$ in the jump intensity kernels.
First, assuming two-sided estimates of the continuous transition density of the
reflected stable-like process $(X_t)_{t \ge 0}$, similarly to
[Q.-Y. Guan and Z.-M. Ma, Probab. Theory Related Fields, 134 (2006),
pp. 649–694],
we obtain the semimartingale decomposition of the process $(X_t)_{t \ge 0}$.
Then by adding more conditions on $\alpha{(\,\cdot\,,\cdot\,)}$, we explicitly
derive upper and lower bound estimates of the Hölder continuous transition
density of $(X_t)_{t \ge 0}$.
Keywords:
semimartingale decomposition, Dirichlet forms, reflected stable-like processes, heat kernel estimates, Hölder continuity.
@article{TVP_2019_64_3_a5,
author = {J. Shin},
title = {Semimartingale decomposition and heat kernel estimates of reflected stable-like processes with variable order},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {526--551},
publisher = {mathdoc},
volume = {64},
number = {3},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a5/}
}
TY - JOUR AU - J. Shin TI - Semimartingale decomposition and heat kernel estimates of reflected stable-like processes with variable order JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2019 SP - 526 EP - 551 VL - 64 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a5/ LA - ru ID - TVP_2019_64_3_a5 ER -
%0 Journal Article %A J. Shin %T Semimartingale decomposition and heat kernel estimates of reflected stable-like processes with variable order %J Teoriâ veroâtnostej i ee primeneniâ %D 2019 %P 526-551 %V 64 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a5/ %G ru %F TVP_2019_64_3_a5
J. Shin. Semimartingale decomposition and heat kernel estimates of reflected stable-like processes with variable order. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 526-551. http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a5/