Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions

A wavelet based linear estimator is proposed for the derivatives of a probability density function based on a sample from a finite mixture of components with varying mixing proportions. It extends the linear estimator of a probability density function proposed by Pokhyl'ko (Theor. Probability and Math. Statist, 70 (2005) 135–145). Upper bounds on L2 and L∞ losses are obtained for such estimators

Nonparametric inference for a class of stochastic partial differential equations based on discrete observations

Consider the stochastic partial differential equations of the type du,(t,x) = (Δu,(t,x)+u,(t,x))dt + ∊ Θ(t) dWQ(t,x), Θ ≤ t ≤ T and du∊,(t,x)= Δu∊ (t,x)dt+ ∊ Θ(t) (I - Δ)-1/2 dW(t,x), 0 ≤ t ≤ T where Δ = ∂2/∂x2,θ ∈ Θ and Θ is a class of positive valued functions such that Θ2(t)∈ L2(R). We obtain an estimator for the function θ(t) based on the Fourier coefficients ui∊(t), 1 ≤ i ≤ N of the random field u∊(t,x) observed at discrete times and study its asymptotic properties

Infinitely divisible characteristic functionals on locally convex topological vector spaces

This article does not have an abstract

On a characteristic property of point processes

This note is concerned with a certain property of point processes. We prove that if N1, N2 and N3 are three independent point processes, then the bivariate point process (N1 + N3, N2 + N3) uniquely determines the point processes N1, N2 and N3

Nonparametric estimation of the derivatives of a density by the method of wavelets

A method of estimation of the derivatives of a probability density using wavelet systems is proposed. Precise order for the integrated mean square of the proposed estimator is obtained

Discrete Gronwall inequalities for demimartingales

The aim of this work is to obtain discrete versions of stochastic Gronwall inequalities involving demimartingale sequences. The results generalize the respective theorems for martingales provided by Kruse and Scheutzow (2018) and Hendy et al. (2022). Moreover, we present an application which provides an upper bound for the a priori estimate of the backward Euler-Maruyama numerical scheme