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Using Theorem 3.4, we have established a necessary and sufficient condition for the existence and the expression of the reflexive re-nonnegative definite solution to matrix
In this section we prove Proposition 2.3 on the representation of the canonical Palm distribution of the historical process and we prove Theorem 3 on the properties of the
One can obtain a new proof of the homogenization result (1.4) from proposition 2.1 by using the fact that Ψ is square integrable on Ω and applying the von Neumann ergodic theorem..
(68) The proofs of the following properties are exactly as those of the corresponding results in [32], and are based primarily on the multiplicative mean ergodic theorem Theorem
We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized gaussian random walk increments.. On a conjecture of R´
As a consequence of Theorem 3.2, Corollary 3.3 and Lemma 3.4, the following result gives the Hausdorff dimension and packing dimension of the intersection of two independent
We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian
Remark 24 Recall that to prove Proposition 8, we used Proposition 1 to establish the fact that if there is a coalescent process satisfying conditions B1 and B2 of Theorem 2, then
