Related papers: Crossing intervals of non-Markovian Gaussian proce…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the…
A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…
The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
We find a representation of the integral of a Gauss-Markov process in the interval [0, t], in terms of Brownian motion. Moreover, some connections with first-passagetime problems are discussed, and some examples are reported.
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…
In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal r.v. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…
We study the fractal properties of the distances between consecutive primes. The distance sequence is found to be well described by a non-stationary exponential probability distribution. We propose an intensity-expansion method to treat…
We study the behavior of independent and stationary increments jump processes as they approach fixed thresholds. The exact crossing time is unavailable because the real-time information about successive jumps is unknown. Instead, the…
This paper concerns the instantaneous frequency (IF) of continuous-time, zero-mean, complex-valued, proper, mean-square differentiable nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for…
Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…