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The Second Construction Theorem
Theory of Minimal Nonnegative Solutions for Systems
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1-bounded equations a(co ae(dX)e atomic almost closed boundary theory called Cauchy sequence Chapter cikxk closed set coeQ Corollary deduce Definition denote density matrix Denumerable Markov Processes determined uniquely distribution and moments dX)e equations xt excessive function exist infinitely F-type Q-process first-type system flying point harmonic function harmonic measure Hence homogeneous denumerable Markov i,jeE ieE jeE Lemma linearly independent Markov chain Markov property matrix of order minimal nonnegative solution minimal process N-B-type necessary and sufficient nonnegative linear equations normal system O-type obtain pij(t probability space processes of order proof of Theorem pseudo-normal system Q is conservative Q is nonconservative Q-matrix is given Q-process is unique random variable second-type strictly nonhomogeneous equations sufficient condition Suppose a Q-matrix system of 1-bounded system of equations system of homogeneous system of nonnegative system of strictly transition probability matrix unique ordinary X(co zero solution