相关论文: A copula-based method to build diffusion models wi…

We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…

In some areas of knowledge there are data representing directions restricted to a specific range of values. Consequently, it is useful to have models for describing variables defined in subsets of the k-dimensional unit sphere. This need…

We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…

Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…

Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…

We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…

Our purpose is to model the dependence between two random variables, taking into account a priori knowledge on these variables. For example, in many applications (oceanography, finance...), there exists an order relation between the two…

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…

Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper demonstrates some difficulties with using copulas even for…

The beta distribution serves as a canonical tool for modeling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent…

The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a…

Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…

We analyse the ultrasound waves reflected by multiple bubbles in the linearized time-dependent acoustic model. The generated time-dependent wave field is estimated close to the bubbles. The motivation of this study comes from the therapy…

Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, L\'evy copulas and zero-mixed models, often face practical difficulties in simulation and…

Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of…

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…