Related papers: Donald Burkholder's work in martingales and analys…
This is a brief overview of the basic techniques of Boolean valued analysis.
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the…
We present a new proof of the Burkholder-Davis-Gundy inequalities for $1\leq p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a…
A retrospective of Martin Schwarzschild's work on galaxy dynamics.
We study stability estimates for the almost extremal functions associated with the $L^p$-bound for the real and imaginary parts of the Beurling-Ahlfors operator. The proof exploits probabilistic methods and rests on analogous results for…
We describe the Bellman function technique for proving sharp inequalities in harmonic analysis. To provide an example along with historical context, we present how it was originally used by Donald Burkholder to prove $L^p$ boundedness of…
In this note we re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde, Journal of Applied Probability, 41(3):654-664, 2004. Some counterexamples are presented and alternative…
We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…
These notes provide a survey of the theory of plane partitions, seen through the glasses of the work of Richard Stanley and his school.
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
Introduction to papers on the modeling and analysis of network data---II
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]