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We first prove two results which both imply that for any sequence B of asymptotic density zero there exists an infinite sequence A such that the sum of any number of distinct
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
The main objective in this section is to prove the following theorem concerning the conditional distribution of the number of edges given the colouring..
de Acosta, Large deviations for vector valued additive functionals of a Markov process: Lower bounds.. Ney, Large deviation lower bounds for arbitrary additive functionals of a
Some deviation inequalities and moderate deviation principles for the maximum likelihood esti- mators of parameters in an Ornstein-Uhlenbeck process with linear drift are established
Using a different approach from some known techniques for self-normalized sum, we establish a Cramér type large deviation result for the maximum of self- normalized sums under a
We now show how the uniform law of large numbers in Theorem 1.1 can be used to prove the hydrodynamic limits for the system of RWRE as stated in Theorem 1.4.. Proof of Theorem 1.4:
We prove some stability results for Picard iteration in uniform space by introducing the concept of an M e -distance as well as using some contractive conditions.. Our
