Abstract
This paper investigates circuit Markov processes under the standpoint of duality principle.
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References
L.V. Ahlfors and L. Sario,Riemann Surfaces, Princeton Univ. Press, Princeton, NJ, (1960), 214–228.
L.V. Ahlfors, Sur le type d'une surface de Riemann,C. R. Acad. Sci. Paris 201 (1935), 30–32.
C.A. Desoer and E.S. Kuh,Basic Circuit Theory, McGraw-Hill International Edition, Singapore, 1969.
R.J. Duffin, Distributed and lumped networks,J. Math. and Mech. 8 (1959), 793–826.
R.J. Duffin, An analysis of the Wang algebra of networks,Trans. Am. Math. Soc. (1959), 114–131.
R.J. Duffin, The extremal length of a network,J. Math. Anal. Appl. 5 (1962), 200–215.
R.J. Duffin, Infinite programs. In “Linear Inequalities and Related Systems,”Ann. Math. Studies, 38 (1956), 157–170.
L. Ford and D.R. Fulkerson, Maximal flow through a network,Can. J. Math. 8 (1956), 399–404.
S. Kalpazidou, On the representation of finite multiple Markov chains by weighted circuits,J. Multivariate Anal. 25 (2) (1988), 241–271.
S. Kalpazidou, On multiple circuit chains with a countable infinity of states,Stoch. Proc. Appl. 31 (1989), 51–70.
S. Kalpazidou,Cycle Representations of Markov Processes, Springer-Verlag, New York, Berlin, Heidelberg, (1995), to appear.
S. Kalpazidou, Asymptotic behavior of sample weighted circuits representing recurrent Markov chains,J. Appl. Prob. 27 (1990), 545–556.
S. Kalpazidou, On Beurling's inequality in terms of thermal power,J. Appl. Prob. 28 (1991).
S. Kalpazidou, Circuit processes and the corresponding one-parameter semigroup of weight operators,J. Theoretical Probab. 5(1) (1992), 205–216.
S. Kalpazidou, Continuous parameter circuit processes with finite state space,Stoch. Proc. Appl. 39 (1991), 301–323.
S. Kalpazidou, On the weak convergence of sequences of circuit processes: A probabilistic approach,J. Appl. Prob. 29 (1992), 374–383.
S. Kalpazidou, Rotational representations of transition matrix functions,Ann. Probability 22(2) (1994), 703–712.
C. St. J.A. Nash-Williams, Random walk and electric current in networks,Proc. Cambridge Philos. Soc. 55 (1959), 181–194.
Qian Minping, Qian Min, and Qian Cheng, Circulation distribution of a Markov chain,Sci. Sinica 25 (1) (1982), 31–40.
Qian Minping and Qian Min, Circulation distribution for recurrent Markov chains,Z. Wahr. Verw. Gab. (1982), 203–210.
J.W.S. Rayleigh, On the approximate solution of certain problems relating to the potential,Proc. London Math. Soc. 7 (1876), 70–75.
A.H. Zemanian, The complete behavior of certain infinite networks under Kirchhoff's node and loop laws,SIAMJ. Appl. Math. 30 (1976), 278–295.
A.H. Zemanian,Infinite Electrical Networks, Cambridge Univ. Press (1991), London-New York.
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Kalpazidou, S. Circuit duality for recurrent Markov processes. Circuits Systems and Signal Process 14, 187–211 (1995). https://doi.org/10.1007/BF01183834
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DOI: https://doi.org/10.1007/BF01183834