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Circulation distribution on groups. (English) Zbl 0728.60014

A condition is given for a symmetric probability measure \(\mu\) on a soluble group G with a random walk generated by \(\mu\) to have a representation by directed circuits. This work is related to that of the author in [J. Appl. Probab. 27, No.3, 545-556 (1990; Zbl 0716.60075)].

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization

Citations:

Zbl 0716.60075
Full Text: DOI

References:

[1] Chung, K. L. (1967).Markov Chains with Stationary Transition Probabilities, Springer, Berlin. · Zbl 0146.38401
[2] Iosifescu, M., and T?utu, P. (1973).Stochastic Processes and Applications in Biology and Medicine, I. Theory, Edit. Acad.-Springer, Bucharest-Berlin.
[3] Kalpazidou, S. (1988). On the representation of finite multiple Markov chains by weighted circuits.J. Multivariate Anal. 25(2), 241-271. · Zbl 0651.60071 · doi:10.1016/0047-259X(88)90050-4
[4] Kalpazidou, S. (1989). On multiple circuit chains with a countable infinity of states.Stochastic Process. Appl. 31, 51-70. · Zbl 0678.60059 · doi:10.1016/0304-4149(89)90102-6
[5] Kalpazidou, S. (1990). Asymptotic behavior of sample weighted circuits representing recurrent Markov chains.J. Appl. Prob. 27, 545-556. · Zbl 0716.60075 · doi:10.2307/3214540
[6] Kalpazidou, S. (1991). Continuous parameter circuit processes with finite state space.Stochastic Process. Appl. (to appear). · Zbl 0736.60062
[7] Qian Minping and Qian Min (1979). The decomposition into a detailed balance part and a circulation part of an irreversible stationary Markov chain.Scientia Sinica, Special Issue II, 69-79. · Zbl 0421.60061
[8] Qian Minping, Qian Min, and Qian Cheng (1982). Circulation distribution of a Markov chain.Scientia Sinica (A) 25, 31-40. · Zbl 0496.60072
[9] Varopoulos, N. Th. (1983). Random walks on soluble groups.Bull. Sci. Math. 107, 337-344. · Zbl 0532.60009
[10] Varopoulos, N. Th. (1983). Brownian motion and transient groups.Ann. Inst. Fourier, Grenoble 33, 241-261. · Zbl 0498.60012
[11] Varopoulos, N. Th. (1984). Brownian motion and random walk on manifolds.Ann. Inst. Fourier, Grenoble 34, 243-269. · Zbl 0523.60071
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