A local limit theorem on the semi-direct product of and
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations
A local time inequality for martingales
A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks.
A lower bound in the law of the iterated logarithm for general lacunary series
We prove a lower bound in a law of the iterated logarithm for sums of the form where f satisfies certain conditions and the satisfy the Hadamard gap condition .
A lower bound on the growth exponent for loop-erased random walk in two dimensions
A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions
The growth exponent α for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius n is of order nα. We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.
A Markov property for two parameter Gaussian processes.
This paper deals with the relationship between two-dimensional parameter Gaussian random fields verifying a particular Markov property and the solutions of stochastic differential equations. In the non Gaussian case some diffusion conditions are introduced, obtaining a backward equation for the evolution of transition probability functions.
A Markov regime-switching marked point process for short-rate analysis with credit risk.
A martingale approach to general Franklin systems
We prove unconditionality of general Franklin systems in , where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.
A martingale approach to some Wiener-Hopf problems, I
A martingale approach to some Wiener-Hopf problems, II
A martingale central limit theorem
A martingale control variate method for option pricing with stochastic volatility
A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility...
A martingale on the zero-set of a holomorphic function.
A martingale proof of the Khinchin iterated logarithm law for Wiener processes
A martingale proof of the theorem by Jessen, Marcinkiewicz and Zygmund on strong differentiation of integrals
A mathematical framework for learning and adaption: (generalized) random systems with complete connections.
The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.
A mathematical model of an In Vitro experiment to investigate endothelial cell migration.
A matrix representation of the Bercovici-Pata bijection.