Related papers: A duration-augmented binary Markov chain for rainf…
This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…
Environmental phenomena are influenced by complex interactions among various factors. For instance, the amount of rainfall measured at different stations within a given area is shaped by atmospheric conditions, orography, and physics of…
This paper develops a comprehensive Markov-based framework for modelling reservoir behaviour and assessing key performance measures such as reliability and resilience. We first formulate a stochastic model for a finite-capacity dam,…
We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so introduced…
Precipitation is a large-scale, spatio-temporally heterogeneous phenomenon, with frequent anomalies exhibiting unusually high or low values. We use Markov Random Fields (MRFs) to detect spatio-temporally coherent anomalies in gridded annual…
Many physical processes involve spatio-temporal observations, which can be studied at different spatial and temporal scales. For example, rainfall data measured daily by rain gauges can be considered at daily, monthly or annual temporal…
There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…
Recent advances in time series research facilitate the development of foundation models. While many state-of-the-art time series foundation models have been introduced, few studies examine their effectiveness in specific downstream…
We present a system for online probabilistic event forecasting. We assume that a user is interested in detecting and forecasting event patterns, given in the form of regular expressions. Our system can consume streams of events and forecast…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random…
Climate change poses complex challenges, with extreme weather events becoming increasingly frequent and difficult to model. Examples include the dynamics of Combined Sewer Systems (CSS). Overburdened CSS during heavy rainfall will overflow…
Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete…
The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…
In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph…
Herein, the Hidden Markov Model is expanded to allow for Markov chain observations. In particular, the observations are assumed to be a Markov chain whose one step transition probabilities depend upon the hidden Markov chain. An…
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…
In the first part of our study, we demonstrated how a simple physical benchmark model can be used to assess assumptions of the conceptual models, based on a lumped Probability Distributed Model (PDM) formulated by Lamb (1999). In this…