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The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…
The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map.…
We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations…
We consider a structural model where the survival/default state is observed together with a noisy version of the firm value process. This assumption makes the model more realistic than most of the existing alternatives, but triggers…
This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
We propose a dynamic model of dependence structure between financial institutions within a financial system and we construct measures for dependence and financial instability. Employing Markov structures of joint credit migrations, our…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
Credit risk assessment increasingly relies on diverse sources of information beyond traditional structured financial data, particularly for micro and small enterprises (mSEs) with limited financial histories. This study proposes a…
The human microbiome is a complex ecological system, and describing its structure and function under different environmental conditions is important from both basic scientific and medical perspectives. Viewed through a biostatistical lens,…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
Strategies aimed at reducing the negative effects of long-term uncertainty and risk are common in biology, game theory, and finance, even if they entail a cost in terms of mean benefit. Here, we focus on the single mutant's invasion of a…
Ecosystems, which are intricate amalgams of biological communities and their surrounding environments, continually evolve under the influence of their myriad interactions. The world is currently facing intensifying environmental…
As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…
The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than…