Weighted Poincaré inequalities on convex domain

Mathematical Research Letters175993-101

Sharp conditions for weighted 1-dimensional Poincaré inequalities

Indiana University Mathematics Journal491143-17

Estimates of best constants for weighted poincaré inequalities on convex domains

10.1017/S0024611506015826Proceedings of the London Mathematical Society931197-22

A note on sharp 1-dimensional poincaré inequalities

10.1090/S0002-9939-06-08545-5Proceedings of the American Mathematical Society13482309-231

Self-improving properties of inequalities of Poincaré type on measure spaces and applications

10.1016/j.jfa.2008.05.012Journal of Functional Analysis255112977-3007JFUA

Harnack's inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients

We continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form div(A(x,u, 07;u))=B(x,u, 07;u)for x 08\u3a9 as considered in our paper Monticelli etal. (2012). There we proved only local boundedness of weak solutions. Here we derive a version of Harnack's inequality as well as local H\uf6lder continuity for weak solutions. The possible degeneracy of an equation in the class is expressed in terms of a nonnegative definite quadratic form associated with its principal part. No smoothness is required of either the quadratic form or the coefficients of the equation. Our results extend ones obtained by J. Serrin (1964) and N. Trudinger (1967) for quasilinear equations, as well as ones for subelliptic linear equations obtained in Sawyer and Wheeden (2006, 2010)

Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients

We derive local boundedness estimates for weak solutions of a large class of second-order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its principal part and require no smoothness of its coe cients. The class includes second-order linear elliptic equations as studied by Gilbarg-Trudinger (1998) and second-order subelliptic linear equations as studied by Sawyer-Wheeden (2006, 2010). Our results also extend ones obtained by J. Serrin (1964) concerning local boundedness of weak solutions of quasilinear elliptic equations

Pricing and Hedging of CDOs: A Top Down Approach

This paper considers the pricing and hedging of collateralized debt obligations (CDOs). CDOs are complex derivatives on a pool of credits which we choose to analyse in the top down model proposed in Filipovic et al. (Math. Finance, forthcoming, 2009). We reflect on the implied forward rates and bring them in connection with the top-down framework in Lipton and Shelton (Working paper, 2009) and Schonbucher (Working paper, ETH Zurich, 2005). Moreover, we derive variance-minimizing hedging strategies for hedging single tranches with the full index. The hedging strategies are given for the general case. We compute them also explicitly for a parsimonious one-factor affine model

Estimating the intensity of a cyclic Poisson process in the presence of linear trend

Cyclic Poisson process, Intensity function, Linear trend, Nonparametric estimation, Consistency, Bias, Variance, Mean-squared error,