57,487 research outputs found
Sample path properties of the stochastic flows
We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi-point motion
Bandlimited Spatial Field Sampling with Mobile Sensors in the Absence of Location Information
Sampling of physical fields with mobile sensor is an emerging area. In this
context, this work introduces and proposes solutions to a fundamental question:
can a spatial field be estimated from samples taken at unknown sampling
locations?
Unknown sampling location, sample quantization, unknown bandwidth of the
field, and presence of measurement-noise present difficulties in the process of
field estimation. In this work, except for quantization, the other three issues
will be tackled together in a mobile-sampling framework. Spatially bandlimited
fields are considered. It is assumed that measurement-noise affected field
samples are collected on spatial locations obtained from an unknown renewal
process. That is, the samples are obtained on locations obtained from a renewal
process, but the sampling locations and the renewal process distribution are
unknown. In this unknown sampling location setup, it is shown that the
mean-squared error in field estimation decreases as where is the
average number of samples collected by the mobile sensor. The average number of
samples collected is determined by the inter-sample spacing distribution in the
renewal process. An algorithm to ascertain spatial field's bandwidth is
detailed, which works with high probability as the average number of samples
increases. This algorithm works in the same setup, i.e., in the presence of
measurement-noise and unknown sampling locations.Comment: Submitted to IEEE Trans on Signal Processin
Statistics of soliton-bearing systems with additive noise
We present a consistent method to calculate the probability distribution of
soliton parameters in systems with additive noise. Even though a weak noise is
considered, we are interested in probabilities of large fluctuations (generally
non-Gaussian) which are beyond perturbation theory. Our method is a further
development of the instanton formalism (method of optimal fluctuation) based on
a saddle-point approximation in the path integral. We first solve a fundamental
problem of soliton statistics governing by noisy Nonlinear Schr\"odinger
Equation (NSE). We then apply our method to optical soliton transmission
systems using signal control elements (filters, amplitude and phase
modulators).Comment: 4 pages. Submitted to PR
- …