This paper continues the study of Milner's encoding of the lazy-calculus into the-calculus Mil90]. The encoding is shown to give rise to a-model in which, in accordance with the theory of the lazy-calculus, conditional extensionality holds. However, the model is not fully abstract. To obtain full abstraction, the operational equivalence on-terms (applicative bisimulation) is reened. The new rel...

Sometimes we are rudely awakened to this fact when a really catastrophic event happens such as an earthquake with unexpected strength at an unexpected location. That is the gist of non-traditional stochastic modeling: accounting for " unexpected events." Although such events cannot be predicted, they can be modeled. measurement errors, leading to the binomial distribution and in the limit, the ...

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. deduce analytical expressions for stationary occupation probability and mean global first passage times. This general approach allows us characterize effect capacity walk strategies reach a particular target or explore network. Our formalism holds ergodic can be implemen...

This article generalizes the small noise cutoff phenomenon to strong solutions of stochastic heat equation and damped wave over a bounded domain subject additive multiplicative Wiener L\'evy noises in Wasserstein distance. For case, we obtain analogous infinite dimensional results respective finite cases obtained recently by Barrera, H\"ogele Pardo (JSP2021), that is, (stronger) profile for (we...

In this paper, we develop a numerical method for the L\'evy-Fokker-Planck equation with fractional diffusive scaling. There are two main challenges. One comes from two-fold nonlocality, that is, need to apply Laplacian operator power law decay distribution. The other arises long-time/small mean-free-path scaling, which introduces stiffness equation. To resolve first difficulty, use change of va...

This paper provides an extended case study of the cutoff phenomenon for a prototypical class nonlinear Langevin systems with single stable state perturbed by additive pure jump L\'evy noise small amplitude $\varepsilon>0$, where driving process is layered type. Under drift coercivity condition associated family processes $X^\varepsilon$ turns out to be exponentially ergodic equilibrium distribu...

Continued fractions lie at the heart of a number of classical algorithms like Euclid's greatest common divisor algorithm or the lattice reduction algorithm of Gauss that constitutes a 2-dimensional generalization. This paper surveys the main properties of functional operators, |transfer operators| due to Ruelle and Mayer (also following L evy, Kuzmin, Wirsing, Hensley, and others) that describe...

The emerging sub eld of econophysics explores the degree to which certain concepts and methods from statistical physics can be appropriately modi ed and adapted to provide new insights into questions that have been the focus of interest in the economics community. Here we give a brief overview of two examples of research topics that are receiving recent attention. A rst topic is the characteriz...