Continuous-time Markov Chains: An Applications-oriented Approach

absorbing analytic assume b₁ backward equations birth and death C₁ Chapman-Kolmogorov equation coefficients communicating class condition continuous-time Markov chains Convergence Theorem death process define Definition denote distribution E₁ ergodic example exists fact Feller fi(t fij(t finite forward equations given Hence holds honest i₁ integers irreducible j₁ jump chain l₁ Laplace transform Lemma m₁ Markov property matrix minimal Q-function minimal solution Monotone Convergence Theorem non-negative solution Note numbers orthogonal orthogonal polynomials P₁ P₁(t P₁j(t Pi(t Pij(t polynomials positive recurrent Prob probability measure PROOF Proposition 3.1 Q is conservative q-matrix q-matrix Q random variables result Reuter satisfies semigroup sequence space statements are equivalent Stieltjes moment problem stochastically monotone supie Suppose t₁ transition function transition function P₁,(t transition probabilities unique vector weakly symmetric zero µ-subinvariant μη Σ Σ