In this paper, we develop a large deviations principle for stochastic delay equations driven by small multiplicative white noise. Both upper and lower large deviations estimates are established.

We solve stochastic differential equations involving the Malliavin derivative and the fractional Malliavin derivative by means of a chaos expansion on a general white noise space (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise space). There exist unitary mappings between the Gaussian and Poissonian white noise spaces, which can be applied in solving SDEs.

The detection and estimation of machine vibration multiperiodic signals of unknown periods in white Gaussian noise is investigated. New estimates for the subsignals (signals making up the received signal) and their periods are derived using an orthogonal subspace decomposition approach. The concept of exactly periodic signals is introduced. This in turn simplifies and enhances the understanding...

Sharp Adaptive Nonparametric Testing for Sobolev Ellipsoids Michael Nussbaum (joint work with Pengsheng Ji) Consider the Gaussian white noise model in sequence space Yj = fj + n ⇠j , j = 1, 2, ... with signal f = {fj}j=1 and ⇠j ⇠ N (0, 1) independent. For some ⇢, ,M > 0, consider hypotheses of ”no signal” vs. an ellipsoid with l2-ball removed: H0 : f = 0 against Ha : f 2 ⌃( ,M) \B⇢,

We give a short introduction to the white noise theory for multiparameter Lévy processes and its application to stochastic partial differential equations driven by such processes. Examples include temperature distribution with a Lévy white noise heat source, and heat propagation with a multiplicative Lévy white noise heat source.