| Wu Chenxun,Guo Maozheng.[J].数学年刊A辑,1980,1(3-4):523~540 |
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| THE STATIONARY DIFFUSION PROCESSES GENERATED BY SECOND ORDER DIFFERENTIAL OPERATIONS AND THEIR PROBABILITY CURRENTS |
| Received:December 15, 1979 |
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| In this paper,we are concerned with the stationary Markov processes generated by second order differential operators under the local boundary conditions, It is proved that all those processes have constnt probability currents, known as circulations of the processes, and hence the processes are called single circulation processes. The invariant measures and the circulation values of those processes are calculated in all cases of boundary classification. It is shown that thr circulation value is an elementary characteristic of irreversible stationary Markov processes and that all the reversible Markov processes in the same problem are just the special ones of the single circulation processes whose circulation values are equal to zero and whose ergodic limits in the sense of weak convergence are not trivial. |
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