5 papers
A tail estimate for empirical processes of multivariate Gaussian under general dependence
Wen Huo, Yasutaka Shimizu
In this paper, we discuss the convergence rate of empirical processes of Gaussian processes for a large class of function families. Our main goal is to show that the tail of the un…
Statistical inference for discretely sampled stochastic functional differential equations with small noise
Hiroki Nemoto, Yasutaka Shimizu
Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an inte…
Asymptotic normality of least squares estimators to stochastic differential equations driven by fractional Brownian motions
Yasutaka Shimizu, Shohei Nakajima
We will consider the following stochastic differential equation (SDE): \begin{equation} X_t=X_0+\int_0^tb(X_s,θ_0)ds+σB_t,~~~t\in(0,T], \end{equation} where is a…
Confidence intervals of ruin probability under Lévy surplus
Yasutaka Shimizu
The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a Lévy process. Assuming a parametric family fo…
Least squares estimators for discretely observed stochastic processes driven by small Levy noises
Hongwei Long, Yasutaka Shimizu, Wei Sun
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving…