We consider the calibration of a Lévy process with American vanilla options. The price of an American vanilla option as a function of the maturity and the strike satisfies a forward in time linear complementarity problem involving a partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process amounts to solving an...

In this paper, the different parameter estimation methods such as maximum likelihood method, least square method, weighted least square method, moments method, the method based on quantiles and maximum spacing method for the Weibull distribution which are widely accepted in wind power studies are presented and discussed. The effect of the selecting parameter estimation method on the estimation ...

To make use of the sparsity property of broadband multipath wireless communication channels, we mathematically propose an l p -norm-constrained proportionate normalized least-mean-square (LP-PNLMS) sparse channel estimation algorithm. A general l p -norm is weighted by the gain matrix and is incorporated into the cost function of the proportionate normalized least-mean-square (PNLMS) algorithm....

The time of arrival (TOA) and the time difference of arrival (TDOA) measurements are transformable to each other without a loss of information regarding positioning and thus the position estimations based on them should be theoretically equivalent. It is proved by Shin [1] in case of homogeneous and uncorrelated ranging sources with the weighted least square (WLS) method. In this paper, their e...