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Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
We present a version of the stochastic maximum principle (SMP) for ergodic control problems. In particular we give necessary (and sufficient) conditions for optimality for controlled dissipative systems in finite dimensions. The strategy we…
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
Markov State Models (MSM) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations, for example…
We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…
We consider SDEs with (distributional) drift in negative Besov spaces and random initial condition and investigate them from two different viewpoints. In the first part we set up a martingale problem and show its well-posedness.We then…
We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal, heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely…
We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
We consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity ($L^p$-regularity in the velocity-variable and Sobolev regularity in the…
This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$. In…
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning…
In this paper we introduce the idea of probability in the definition of Sequential Dynamical Systems, thus obtaining a new concept, Probabilistic Sequential System. The introduction of a probabilistic structure on Sequential Dynamical…
A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. There has been given the connection between conditions of superstability…