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We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features.…
It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\'echet and…
Mixing by incompressible flows is a ubiquitous yet incompletely understood phenomenon in fluid dynamics. While previous studies have focused on optimal mixing rates, the question of its genericity, i.e., whether mixing occurs for typical…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…
We study the rate of weak convergence of Markov chains to diffusion processes under suitable but quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree…
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential…
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated…
In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak monotone condition, it was demonstrated in a previous paper…
For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the…
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole. The presence of the latter influences the extremal index…
We consider a partially hyperbolic set $K$ on a Riemannian manifold $M$ whose tangent space splits as $T_K M=E^{cu}\oplus E^{s}$, for which the centre-unstable direction $E^{cu}$ expands non-uniformly on some local unstable disk. We show…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…