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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.

Chigansky, P., Liptser, R., Bobrovsky, B.Z. (2001)

Journal of Applied Mathematics and Stochastic Analysis

A simple card guessing game revisited.

Knopfmacher, Arnold, Prodinger, Helmut (2001)

The Electronic Journal of Combinatorics [electronic only]

A simple characterization of almost uniform convergence by stochastic convergence.

D. Pachky (1990)

Manuscripta mathematica

A simple example concerning the global Markov Property of lattice random fields

von Weizsäcker, Heinrich (1980)

Abstracta. 8th Winter School on Abstract Analysis

A simple fluctuation lower bound for a disordered massless random continuous spin model in $d = 2$ .

Külske, Christof, Orlandi, Enza (2006)

Electronic Communications in Probability [electronic only]

A simple formula for an analogue of conditional Wiener integrals and its applications. II

Dong Hyun Cho (2009)

Czechoslovak Mathematical Journal

Let $C [0, T]$ denote the space of real-valued continuous functions on the interval $[0, T]$ with an analogue $w_{ϕ}$ of Wiener measure and for a partition $0 = t_{0} < t_{1} < \dots < t_{n} < t_{n + 1} = T$ of $[0, T]$ , let $X_{n} C [0, T] \to ℝ^{n + 1}$ and $X_{n + 1} C [0, T] \to ℝ^{n + 2}$ be given by $X_{n} (x) = (x (t_{0}), x (t_{1}), \dots, x (t_{n}))$ and $X_{n + 1} (x) = (x (t_{0}), x (t_{1}), \dots, x (t_{n + 1}))$ , respectively. In this paper, using a simple formula for the conditional $w_{ϕ}$ -integral of functions on $C [0, T]$ with the conditioning function $X_{n + 1}$ , we derive a simple formula for the conditional $w_{ϕ}$ -integral of the functions with the conditioning function $X_{n}$ . As applications of the formula with the function $X_{n}$ , we evaluate the conditional $w_{ϕ}$ -integral...

A simple interpretation of two stochastic processes subject to an independent death process.

Gani, Joseph, Swift, Randall J. (2009)

Applied Mathematics E-Notes [electronic only]

A simple proof of a theorem of Blackwell and Dubins on the maximum of a uniformly integrable martingale

David Gilat, Isaac Meilijson (1988)

Séminaire de probabilités de Strasbourg

A simple proof of a theorem on Markov operators

Antoni Leon Dawidowicz, Andrzej Turski (1988)

Annales Polonici Mathematici

A simple proof of Doob's convergence theorem

Kai Lai Chung (1971)

Séminaire de probabilités de Strasbourg

A simple proof of Fishburn's moments theorem.

María Lina Martínez García (1985)

Trabajos de Estadística e Investigación Operativa

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.