We introduce the smooth total variation distance as a natural choice to establish equivalence. We propose asymptotic and bootstrap-based tests for which asymptotic optimality is shown. The finite sample performance is studied by simulations. Then we apply tests to real data sets. The tests are...

About twenty expansions applicable for a wide range of bivariate copulas are given. These expansions being mostly elementary enable easy computation of measures and properties of copulas.

In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions imposed to covariances, which has interest in itself.

The problem of the optimal intensity of instant observations of the processes of birth and death with linear growth and immigration is considered. Results are obtained for the objective function calculated as an expected normalized linear function of the number of observations and an expected...

This paper considers the problem of estimating a covariance matrix under Stein’s loss. Sufficient conditions for the modified Efron–Morris estimator to be minimax under weighted quadratic loss are shown, which provide a general method for improving the estimator of the covariance matrix.

In this paper, we consider the harmonic measure on the unit sphere Sn−1 on Rn (n≥2) and offer a two-sided estimate of precise order on the Sobolev constant with exponent p∈(1,2). As special cases for p=1 and p tending to 2, our estimates recover those in Barthe et al. (2104) for n≥3...

In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of...

This paper shows an explicit small time expansion formula of expectation of the solution to Young SDEs driven by fractional Brownian motion H1/2. The expansion coefficients are obtained by using Malliavin calculus for fractional Brownian motion. Furthermore, we show an analytically tractable...

The occurrence of rare events can often be well described by a compound Poisson distribution. However, one can only start modelling the occurrence of rare events after such events have happened, thus a conditional compound Poisson distribution is more appropriate in applications. In this note,...

For spectrally negative Lévy processes, we find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (−∞,0) and (0,∞). These expressions are in terms of the associated scale functions and the inverse functions of Laplace exponents.