|
Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 3, Pages 540–547
(Mi tvp736)
|
|
|
|
This article is cited in 15 scientific papers (total in 15 papers)
Short Communications
On a class degenerative diffusion processes
I. M. Sonin Moscow
Abstract:
It is proved that the degenerative diffusion processes with the characteristic operators reducing after a change of variables to the form
\begin{gather*}
Lu=\frac12\sum_{ij=1}^na_{ij}(x_1^1,\dots,x_1^n,x_2^1,\dots,x_2^n,\dots,x_N^1,\dots,x_N^n,t)\frac{\partial^2u}{\partial x_1^i\partial x_1^j}+
\\
+\sum_{i=1}^na_i(x_1^1,\dots,x_N^n,t)\frac{\partial u}{\partial x_1^i}+\sum_{i=1}^nx_1^i\frac{\partial u}{\partial x_2^i}+\sum_{i=1}^nx_2^i\frac{\partial u}{\partial x_3^i}+\dots
\\
\dots+\sum_{i=1}^nx_{N-1}^i\frac{\partial u}{\partial x_N^i}+a(x_1^1,\dots,x_N^n,t)u
\end{gather*}
have smooth densities. The proof is carried out by constructing the fundamental solution of the corresponding parabolic equation. For this the classical method of Lévy with some modifications is used.
Received: 05.05.1966
Citation:
I. M. Sonin, “On a class degenerative diffusion processes”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 540–547; Theory Probab. Appl., 12:3 (1967), 490–496
Linking options:
https://www.mathnet.ru/eng/tvp736 https://www.mathnet.ru/eng/tvp/v12/i3/p540
|
Statistics & downloads: |
Abstract page: | 265 | Full-text PDF : | 120 |
|