Showing papers in "MI Preprint Series in 2016"

Asymptotic profiles for the compressible Navier-Stokes equations on the whole space

Abstract: Abstract This paper is concerned with the large time behavior of strong solutions of the compressible Navier–Stokes equation in the whole space R n ( n ≥ 3 ) around the constant state. It was shown by Kawashima, Matsumura and Nishida (1979) and Hoff and Zumbrun (1995) that the perturbation of the constant state is time-asymptotic to a solution of the linearized problem, that is, a first-order asymptotic profile. In this paper a second-order asymptotic profile of the solution, which is caused by the nonlinear effect, is given.

Non-Gaussian quasi-likelihood estimation of locally stable SDE

Abstract: We address parametric estimation of both trend and scale coefficients of a pure-jump Levy driven univariate stochastic differential equation (SDE) model based on high-frequency data over a fixed time period The conventional Gaussian quasi-maximum likelihood estimator is known to be inconsistent In this paper, under the assumption that the driving Levy process is locally stable, we propose a novel quasi-likelihood function based on the small-time non-Gaussian stable approximation of the unknown transition density The resulting estimator is shown to be asymptotically mixed-normally distributed and remarkably more efficient than the Gaussian quasi-maximum likelihood estimator We need neither ergodicity nor existence of finite moments Compared with the existing methods for estimating SDE models, the proposed quasi-likelihood enables us to achieve better performance in a unified manner for a wide range of the driving Levy processes

Time periodic problem for the compressible Navier-Stokes equation on R^2 with antisymmetry

Abstract: The compressible Navier-Stokes equation is considered on the two dimensional whole space when the external force is periodic in the time variable. The existence of a time periodic solution is proved for sufficiently small time periodic external force with antisymmetry condition. The proof is based on using the time-T -map associated with the linearized problem around the motionless state with constant density. In some weighted L∞ and Sobolev spaces the spectral properties of the time-T -map is investigated by a potential theoretic method and an energy method. The existence of a stationary solution to the stationary problem is also shown for sufficiently small time-independent external force with antisymmetry condition on R2.