diffusion process with jumps, parametric inference, discrete observation, contrast function, asymptotic normality, asymptotic efficiency,

Two types of leaky waves are obtained in this paper. They are the first leaky wave, whose phase velocity is between those of slow and fast shear waves, and the second leaky waves, whose phase velocity is greater than that of the fast shear wave. The characteristics of leaky waves propagating on LiNbO3 and LiTaO3 substrates are theoretically investigated by changing cut angles and propagating directions. Propagation loss of the first leaky wave for an electrically open surface becomes almost zero at φ=20, 40, 80, 100, 140 and 160° on ( φ, 90°, 0°)-cut LiNbO3 substrate, and K 2 is 16.2% at these cuts. Phase velocities of the second leaky waves propagating on (90°, 90°, ψ )-cut LiTaO3 and LiNbO3 substrates are twice as fast as those of Rayleigh waves, and electromechanical coupling coefficient (K 2) of 2.14% is obtained at ψ=31° on the LiTaO3 substrate. Propagation losses of both electrically open and short surfaces are almost zero at ψ=164° on the LiTaO3 substrate. K 2 of as high as 12.9% is obtained at ψ=36° on the LiNbO3 substrate. Propagation losses of both electrically open and short surfaces are almost zero at ψ=163° on the LiNbO3 substrate.

diffusion process with jumps, infinitely many jumps, M-estimation, discrete observation, parametric inference, asymptotic normality, partial efficiency,

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 Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient ε → 0 and n → ∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Lévy process.

No abstract