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THE CANONICAL REPRESENTATION
WEAK CONVERGENCE OF DISTRIBUTIONS
13 other sections not shown
according addition arbitrary associate assumptions belongs bounded bounded sets choose closed cluster field clustering representation coincides compact conclude Consequently considered continuous with respect convergence convolution correspondence countable defined denote derived distri element equation equivalent ergodic everywhere with respect exists finite measures finite sequence given hand Hence holds immediately implies increasing inequality infinitely divisible distribution integers intensity introduced lim sup Matthes means measurable with respect measure H metric monotone natural numbers o-algebra o-finite observe obtain Obviously one-to-one pairwise disjoint sets phase space Poisson positive probability Proof Proposition provides random real function relation satisfying the condition simple Slim statements stationary distribution stationary measure stochastic kernel subset suppose tends Theorem transformed u(dx uniquely v(da valid virtue zero