相关论文: GARCH-extended models: theoretical properties and …
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a…
We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of…
We provide a characterisation of the continuous-time Markov models where the Markov matrices from the model can be parameterised directly in terms of the associated rate matrices (generators). That is, each Markov matrix can be expressed as…
The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a…
We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical…
We introduce the notion of continuously invertible volatility models that relies on some Lyapunov condition and some regularity condition. We show that it is almost equivalent to the ability of the volatilities forecasting using the…
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a…
Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…
In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle.…
Latent feature modeling allows capturing the latent structure responsible for generating the observed properties of a set of objects. It is often used to make predictions either for new values of interest or missing information in the…
Models of dynamic networks --- networks that evolve over time --- have manifold applications. We develop a discrete-time generative model for social network evolution that inherits the richness and flexibility of the class of…
This paper introduces a general Bayesian non- parametric latent feature model suitable to per- form automatic exploratory analysis of heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or…
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…
In this chapter, we present a review of latent position models for networks. We review the recent literature in this area and illustrate the basic aspects and properties of this modeling framework. Through several illustrative examples we…
The mathematical properties associated with the widely accepted concept of the extensivity of many of the common thermodynamic variables are examined and some of their consequences considered. The possible conflict between some of these and…
A criterion of joint ergodicity of several sequences of transformations of a probability measure space $X$ of the form $T_{i}^{\phi_{i}(n)}$ is given for the case where $T_{i}$ are commuting measure preserving transformations of $X$ and…
We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…
In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…