Related papers: Large deviations conditioned on large deviations I…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…
The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…
We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
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…
In this paper we establish a large deviations type estimate for strongly mixing Markov chains with respect to the Lp norm. As applications we derive such estimates for the iterates of a locally constant random cocycle with mixed rank, as…
We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…
Let $\Delta^o$ be a finite set and, for each probability measure $m$ on $\Delta^o$, let $G(m)$ be a transition probability kernel on $\Delta^o$. Fix $x_0 \in \Delta^o$ and consider the chain $\{X_n, \; n \in \mathbb{N}_0\}$ of…
The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
Starting from the overdamped Langevin dynamics in $\mathbb{R}^n$, $$ dX_t = -\nabla V(X_t) dt + \sqrt{2 \beta^{-1}} dW_t, $$ we consider a scalar Markov process $\xi_t$ which approximates the dynamics of the first component $X^1_t$. In the…
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time…