On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations
A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a pseudo-differential operator whose symbol is...
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Vasyl Stefanyk Precarpathian National University
2015-07-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1388 |
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doaj-c644dcee0fb84530b0eba745e4e9bec92020-11-25T02:58:42ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102015-07-017110110710.15330/cmp.7.1.101-1071388On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equationsM.M. Osypchuk0Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineA fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a pseudo-differential operator whose symbol is given by $-c|\lambda|^\alpha$, were the constants $\alpha\in(1,2)$ and $c>0$ are fixed. The vector-valued operator $\mathbf{B}$ has the symbol $2ic|\lambda|^{\alpha-2}\lambda$. We construct a fundamental solution of the equation $u_t=(\mathbf{A}+(a(\cdot),\mathbf{B}))u$ with a continuous bounded vector-valued function $a$.https://journals.pnu.edu.ua/index.php/cmp/article/view/1388stable processcauchy problempseudo-differential equationtransition probability density |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M.M. Osypchuk |
| spellingShingle |
M.M. Osypchuk On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations Karpatsʹkì Matematičnì Publìkacìï stable process cauchy problem pseudo-differential equation transition probability density |
| author_facet |
M.M. Osypchuk |
| author_sort |
M.M. Osypchuk |
| title |
On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations |
| title_short |
On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations |
| title_full |
On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations |
| title_fullStr |
On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations |
| title_full_unstemmed |
On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations |
| title_sort |
on some perturbations of a stable process and solutions to the cauchy problem for a class of pseudo-differential equations |
| publisher |
Vasyl Stefanyk Precarpathian National University |
| series |
Karpatsʹkì Matematičnì Publìkacìï |
| issn |
2075-9827 2313-0210 |
| publishDate |
2015-07-01 |
| description |
A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a pseudo-differential operator whose symbol is given by $-c|\lambda|^\alpha$, were the constants $\alpha\in(1,2)$ and $c>0$ are fixed. The vector-valued operator $\mathbf{B}$ has the symbol $2ic|\lambda|^{\alpha-2}\lambda$. We construct a fundamental solution of the equation $u_t=(\mathbf{A}+(a(\cdot),\mathbf{B}))u$ with a continuous bounded vector-valued function $a$. |
| topic |
stable process cauchy problem pseudo-differential equation transition probability density |
| url |
https://journals.pnu.edu.ua/index.php/cmp/article/view/1388 |
| work_keys_str_mv |
AT mmosypchuk onsomeperturbationsofastableprocessandsolutionstothecauchyproblemforaclassofpseudodifferentialequations |
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1724705581849116672 |