A short proof of the Hausdorff dimension formula for Lévy processes.
A silent-silent duel with randomly detected opponents
A simple approach to functional inequalities for non-local Dirichlet forms
With direct and simple proofs, we establish Poincaré type inequalities (including Poincaré inequalities, weak Poincaré inequalities and super Poincaré inequalities), entropy inequalities and Beckner-type inequalities for non-local Dirichlet forms. The proofs are efficient for non-local Dirichlet forms with general jump kernel, and also work for Lp(p> 1) settings. Our results yield a new sufficient condition for fractional Poincaré inequalities, which were recently studied in [P.T. Gressman,...
A simple asymptotically optimal filter over an infinite horizon.
A simple card guessing game revisited.
A simple characterization of almost uniform convergence by stochastic convergence.
A simple example concerning the global Markov Property of lattice random fields
A simple fluctuation lower bound for a disordered massless random continuous spin model in .
A simple formula for an analogue of conditional Wiener integrals and its applications. II
Let denote the space of real-valued continuous functions on the interval with an analogue of Wiener measure and for a partition of , let and be given by and , respectively. In this paper, using a simple formula for the conditional -integral of functions on with the conditioning function , we derive a simple formula for the conditional -integral of the functions with the conditioning function . As applications of the formula with the function , we evaluate the conditional -integral...
A simple interpretation of two stochastic processes subject to an independent death process.
A simple proof of a theorem of Blackwell and Dubins on the maximum of a uniformly integrable martingale
A simple proof of a theorem on Markov operators
A simple proof of Doob's convergence theorem
A simple proof of Fishburn's moments theorem.
We derive a necessary condition for stochastic dominance of any order based on the Laplace transform of probability measures on [0,∞) for which it follows easily Fishburn's theorem on the lexicographic order of the moments.
A simple proof of Schipp's theorem.
A Simple Proof of the Kinematic Formula.
A simple proof of the continuity of the higher order Riesz transforms with respect to the gaussian measure
A simple proof of the logarithmic Sobolev inequality on the circle
A Simple Proof of the Majorizing Measure Theorem.
A simple proof of the Poincaré inequality for a large class of probability measures.