A simple proof of the support theorem for diffusion processes
A simple remark on the conditioned square functions for martingale transforms
A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls
Negative association for a family of random variables means that for any coordinatewise increasing functions f,g we have for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of...
A simplification in the proof of the non-isomorphism between H¹(δ) and H¹(δ²)
The proof that H¹(δ) and H¹(δ²) are not isomorphic is simplified. This is done by giving a new and simple proof to a martingale inequality of J. Bourgain.
A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons.
A simplified proof of the Sevastyanov theorem on branching processes
A simulation of integral and derivative of the solution of a stochastici integral equation
A stochastic integral equation corresponding to a probability space is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable . One constructs stochastic processes , connected with a Markov chain and with the space . The expected values of (i = 1,2) are respectively the expected value of an integral representation of a solution x(t) of the equation and that of its derivative .
A single-server queue with random accumulation level.
A singular large deviations phenomenon
A singular parabolic Anderson model.
A Skorohod space of discontinuous functions on a general set
A solution of an equation for indexed functions
A solution of the D'Alembert's functional equation on a locally compact Abelian group.
A solution of the functional equation ...(x-y) = ...aj(x)... On a locally compact Abelian group. (Short Communication).
A special set of exceptional times for dynamical random walk on .
A species sampling model with finitely many types.
A spectral approach to compute the mean performance measures of the queue with low-order BMAP input.
A square root filter for real time multivariate regression
A stability theorem for elliptic Harnack inequalities
We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.
A stationary random graph of no growth rate
We present a random automorphism-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.