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I am very grateful to the anonymous referee for his valuable comments (incorporated into the current presentation as Re- marks 1–3), providing the proof of Lemma 5 and
For the proof of Lemma 3 below we need a few facts on (ho- mogeneous) linear recurrence sequences with constant coefficients, for short... Indeed, we may even
It is very similar to the proof of Lemma 4 in Kesten (1987), which deals with the probability of four disjoint paths to ∆S(n), two occupied ones and two vacant ones, with 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..
We shall make frequent use of the following inclusion-exclusion type lemma.. The well-known proof is easy, but so short that we include it. It would then follow from Fubini’s
We show that Varadhan’s small time asymptotics for densities of the solution of a stochastic differ- ential equation in R n [8] carries over to a Hilbert space-valued
Keywords Catalyst, reactant, measure-valued branching, interactive branching, state-dependent branch- ing, two-dimensional process, absolute continuity, self-similarity,
In this section we prove a fixed point theorem in a complete metric space by employing notion of generalized w-distance.. The following Lemma is crucial in the proof of
