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We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…
Hydroelectric power generation is a critical component of the global energy matrix, particularly in countries like Brazil, where it represents the majority of the energy supply. However, its strong dependence on river discharges, which are…
We consider a discrete-time Markov chain $(X^t,Y^t)$, $t=0,1,2,...$, where the $X$-component forms a Markov chain itself. Assume that $(X^t)$ is Harris-ergodic and consider an auxiliary Markov chain ${\hat{Y}^t}$ whose transition…
We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain…
Short-term water demand forecasting (StWDF) is the foundation stone in the derivation of an optimal plan for controlling water supply systems. Deep learning (DL) approaches provide the most accurate solutions for this purpose. However, they…
Variable renewable energy droughts, so called Dunkelflaute events, emerge as a challenge for climate-neutral energy systems based on variable renewables. Here we characterize European drought events for on- and offshore wind power, solar…
Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
For modeling extreme rainfall, the widely used Brown-Resnick max-stable model extends the concept of the variogram to suit bloc maxima, allowing the explicit modeling of the extremal dependence shown by the spatial data. This extremal…
Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the…
Accurate stochastic simulations of hourly precipitation are needed for impact studies at local spatial scales. Statistically, hourly precipitation data represent a difficult challenge. They are non-negative, skewed, heavy tailed, contain a…
The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the…
We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…
Long-term rainfall prediction is a challenging task especially in the modern world where we are facing the major environmental problem of global warming. In general, climate and rainfall are highly non-linear phenomena in nature exhibiting…
Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to…
The increasing frequency of extreme weather events has posed significant risks to the operation of power grids. During long-duration extreme weather events, microgrid formation (MF) is an essential solution to enhance the resilience of the…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates which are functions with suitable…
We develop new flexible univariate models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for threshold exceedances. These models can accommodate departure from…