Weak Derivatives Research Articles

Robust Frequency Estimation of Multi-sinusoidal Signals Using Orthogonal Matching Pursuit with Weak Derivatives Criterion

In this paper, the weak derivatives (WD) criterion is introduced to solve the frequency estimation problem of multi-sinusoidal signals corrupted by noises. The problem is therefore modeled as a new least squares optimization task combined with WD. To overcome the potential basis mismatch effect caused by discretization of the frequency parameters, a modified orthogonal matching pursuit algorithm is proposed to solve the optimization problem by coupling it with a novel multi-grid dictionary training strategy. The proposed algorithm is validated on a set of simulated datasets with white noise and stationary colored noise. The comprehensive simulation studies show that the proposed algorithm can achieve more accurate and robust estimation than state-of-the-art algorithms.

Efficient price sensitivity estimation of financial derivatives by weak derivatives

The stochastic gradient estimation method of weak derivatives (WD) is presented with the aim of constructing efficient algorithms for the estimation of the “Greeks” of financial derivatives. The key idea is to replace the derivative of the probability measure of the underlying model by its WD. The WD method has the same advantageous property of the well-known score function method that the form of the Greek estimator does not depend on the details of the payoff function but only on the probability density of the underlying model. Simulation studies indicate that the WD estimator has significantly lower variance than the score function and finite difference estimator, however, the associated computational burden in certain cases may not be negligible.

A note on the relation between weak derivatives and perturbation realization

Studies the relationship between two important approaches in perturbation analysis (PA)-perturbation realization (PR) and weak derivatives (WDs). Specifically, we study the relation between PR and WDs for estimating the gradient of stationary performance measures of a finite state-space Markov chain. We show that the WDs expression for the gradient of a stationary performance measure can be interpreted as the expected PR factor where the expectation is carried out with respect to a distribution that is given through the weak derivative of the transition kernel of the Markov chain. Moreover, we present unbiased gradient estimators.

A note on the relation between weak derivatives and perturbation realization

Studies the relationship between two important approaches in perturbation analysis (PA)-perturbation realization (PR) and weak derivatives (WDs). Specifically, we study the relation between PR and WDs for estimating the gradient of stationary performance measures of a finite state-space Markov chain. We show that the WDs expression for the gradient of a stationary performance measure can be interpreted as the expected PR factor where the expectation is carried out with respect to a distribution that is given through the weak derivative of the transition kernel of the Markov chain. Moreover, we present unbiased gradient estimators.