相关论文: Harris Processes
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work,…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments…
We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…
The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…
In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The…
We introduce a technique to merge two biased Brownian motions into a single regular process. The outcome follows a stochastic differential equation with a constant diffusion coefficient and a non-linear drift. The emerging stochastic…
We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…
In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…
Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…