Related papers: Adaptive sampling of large deviations
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
We introduce multi-kangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functionals. We calculate analytically the large deviation properties. Applications include zero-crossing statistics…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
Adaptive time series forecasting is essential for prediction under regime changes. Several classical methods assume linear Gaussian state space model (LGSSM) with variances constant in time. However, there are many real-world processes that…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…
We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent…
We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of "linear response function" in the general framework of Markov processes. We show that for processes…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…