Special solutions of the Chapman–Kolmogorov equation for multidimensional-state Markov processes with continuous time
| Autor: | Roman N. Miroshin |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Markov kernel Markov chain General Mathematics 010102 general mathematics Mathematical analysis Markov process 01 natural sciences Time reversibility 03 medical and health sciences symbols.namesake 030104 developmental biology Markov renewal process Balance equation symbols Applied mathematics Markov property 0101 mathematics Chapman–Kolmogorov equation Mathematics |
| Zdroj: | Vestnik St. Petersburg University: Mathematics. 49:122-129 |
| ISSN: | 1934-7855 1063-4541 |
| Popis: | The bilinear Chapman–Kolmogorov equation determines the dynamical behavior of Markov processes. The task to solve it directly (i.e., without linearizations) was posed by Bernstein in 1932 and was partially solved by Sarmanov in 1961 (solutions are represented by bilinear series). In 2007–2010, the author found several special solutions (represented both by Sarmanov-type series and by integrals) under the assumption that the state space of the Markov process is one-dimensional. In the presented paper, three special solutions have been found (in the integral form) for the multidimensional- state Markov process. Results have been illustrated using five examples, including an example that shows that the original equation has solutions without a probabilistic interpretation. |
| Databáze: | OpenAIRE |
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