Estimating a function from ergodic samples with additive noise

Estimating a Fun tion from Ergodi Samples with Additive Noise

Estimating a Concave Distribution Function from Data Corrupted with Additive Noise

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0,∞). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational algorithm. For the LS estimator and its derivative, we als...

Recovering Convex Boundaries from Blurred and Noisy Observations1 by Alexander Goldenshluger

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the s...

1 3 N ov 2 00 1 UNIFORM EXPONENTIAL ERGODICITY OF STOCHASTIC DISSIPATIVE SYSTEMS

We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in R d with d ≤ 3.

A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H > 1/2. The estimator is based on discrete time observations of the stochastic differential equation, and using tools from ergodic theory and stochastic analysis we derive its strong consistency.