A remark on Tsirelson's stochastic differential equation
A remarkable -finite measure unifying supremum penalisations for a stable Lévy process
The -finite measure which unifies supremum penalisations for a stable Lévy process is introduced. Silverstein’s coinvariant and coharmonic functions for Lévy processes and Chaumont’s -transform processes with respect to these functions are utilized for the construction of .
A representation of infinitely divisible signed random measures.
A representation result for time-space brownian chaos
A reversibility problem for Fleming-Viot processes.
A Riemann approach to random variation
This essay outlines a generalized Riemann approach to the analysis of random variation and illustrates it by a construction of Brownian motion in a new and simple manner.
A second order SDE for the Langevin process reflected at a completely inelastic boundary
It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
A semimartingale characterization of average optimal stationary policies for Markov decision processes.
A sharp analysis on the asymptotic behavior of the Durbin–Watson statistic for the first-order autoregressive process
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin–Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise....
A sharp maximal inequality for continuous martingales and their differential subordinates
Assume that , are continuous-path martingales taking values in , , such that is differentially subordinate to . The paper contains the proof of the maximal inequality The constant is shown to be the best possible, even in the one-dimensional setting of stochastic integrals with respect to a standard Brownian motion. The proof uses Burkholder’s method and rests on the construction of an appropriate special function.
A Sharper Form of the Doeblin-Lévy-Kolmogorov-Rogozin Inequality for Concentration Functions.
A short proof of decomposition of strongly reduced martingales
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 proof of a theorem of Blackwell and Dubins on the maximum of a uniformly integrable martingale
A simple proof of Schipp's theorem.
A Simple Proof of the Majorizing Measure Theorem.
A simple proof of the Poincaré inequality for a large class of probability measures.