We consider a two-scaled diffusion system, when drift and diffusion parameters of the “slow” component are contaminated by the "fast" unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the "slow" component w.r.t. the...

We consider a two-scaled diffusion system, when drift and diffusion parameters of the 'slow' component are contaminated by the ' fast' unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the 'slow' component w.r.t. the...

We consider a two-scaled diffusion system, when drift and diffusion parameters of the 'slow' component are contaminated by the ' fast' unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the 'slow' component w.r.t. the...

Let Mt be a vector martingale and <M>t denote its predictable quadratic variation. In this paper we present a bound for the probability that with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is...</m>