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A lower bound for the principal eigenvalue of the Stokes operator in a random domain

V. V. Yurinsky (2008)

Annales de l'I.H.P. Probabilités et statistiques

This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...

A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions

Gregory F. Lawler (2010)

ESAIM: Probability and Statistics

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 Malliavin calculus method to study densities of additive functionals of SDE’s with irregular drifts

Arturo Kohatsu-Higa, Akihiro Tanaka (2012)

Annales de l'I.H.P. Probabilités et statistiques

We present a general method which allows to use Malliavin Calculus for additive functionals of stochastic equations with irregular drift. This method uses the Girsanov theorem combined with Itô–Taylor expansion in order to obtain regularity properties for this density. We apply the methodology to the case of the Lebesgue integral of a diffusion with bounded and measurable drift.

A Markov property for two parameter Gaussian processes.

David Nualart Rodón, M. Sanz (1979)

Stochastica

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 martingale approach to general Franklin systems

Anna Kamont, Paul F. X. Müller (2006)

Studia Mathematica

We prove unconditionality of general Franklin systems in L p ( X ) , where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han (2007)

ESAIM: Probability and Statistics

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...

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