Related papers: Coexistence in stochastic spatial models
The concept of spatial confounding is closely connected to spatial regression, although no general definition has been established. A generally accepted idea of spatial confounding in spatial regression models is the change in fixed effects…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all…
We investigate spatial confounding in the presence of multivariate disease dependence. In the "analysis model perspective" of spatial confounding, adding a spatially dependent random effect can lead to significant variance inflation of the…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
The problem of the equivalence of the spherical and mean spherical models, which has been thoroughly studied and understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench…
We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of…
Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both…
The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial…
Many natural ecosystems harbor large numbers of coexisting species competing for far fewer distinct resources, in apparent defiance of the competitive exclusion principle. Various mechanisms have been proposed to explain this apparent…
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…
When confronting a spatio-temporal regression, it is sensible to feed the model with any available prior information about the spatial dimension. For example, it is common to define the architecture of neural networks based on spatial…
We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are…
In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the…
Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in one…
I argue that ``good'' mathematical models of spatio-temporal dynamics in two-dimensions require non-local operators in the nonlinear terms. Consequently, the often used Swift-Hohenberg equation requires modification as it is purely local.…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed…