Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : Hölder continuity. 
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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/

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