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We show that if ψ(A) = ψ(B) is satisfied then many properties enjoyed by nonsingular borderings have analogs for singular (or rectangular) borderings as well.. This
Necessary and sufficient conditions are established for a group of mixed-type reverse- order laws for generalized inverses of a triple matrixproduct to hold.. Some applications of
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
Let ψ and W be as described in the second part of the statement of the theorem and let φ denote the Laplace exponent of the descending ladder height subordinator associated to
We use a coupling method for functional stochastic differential equations with bounded memory to establish an analogue of Wang’s dimension-free Harnack inequality [ 13 ].. The
We present a tail inequality for suprema of empirical processes generated by vari- ables with finite ψ α norms and apply it to some geometrically ergodic Markov chains to derive
Ose ¸kowski, Sharp weak type inequalities for differentially subordinated martingales, Bernoulli 15 Vol. Suh, A sharp weak type (p, p) inequality (p > 2) for martingale
The following lemma gives a lower bound on the range of a random homomorphism of C n,k with exactly ℓ non-constant layers.
