Geodesic
On constructing a sticky membrane located on a~given surface for a~symmetric $\alpha$-stable process
Teoriâ slučajnyh processov, Tome 23 (2018) no. 1, pp. 66-72

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For a symmetric $\alpha$-stable stochastic process with $\alpha\in(1,2)$ in a Euclidean space, a membrane located on a fixed bounded closed surface $S$ is constructed in such a way that the points of the surface possess the property of delaying the process with some given positive coefficient $(p(x))_{x\in S}$. In other words, the points of $S$ are sticky for the process constructed. We show that this process is associated with some initial-boundary value problem for pseudo-differential equations related to a symmetric $\alpha$-stable process.
Keywords: Stable process, Random change of time, Initial-boundary value problem, Pseudo-differential equation.
Mots-clés : Membranes, Feynman-Kac formula 
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     author = {M. M. Osypchuk and M. I. Portenko},
     title = {On constructing a sticky membrane located on a~given surface for a~symmetric $\alpha$-stable process},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {66--72},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2018_23_1_a4/}
}
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M. M. Osypchuk; M. I. Portenko. On constructing a sticky membrane located on a~given surface for a~symmetric $\alpha$-stable process. Teoriâ slučajnyh processov, Tome 23 (2018) no. 1, pp. 66-72. http://geodesic.mathdoc.fr/item/THSP_2018_23_1_a4/