Related papers: Variational principles for asymptotic variance of …

We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…

We consider a generalization of the model by Doering and Gadoua to non-Markovian potential-switching generated by arbitrary renewal processes. For the Markovian switching process, we extend the original results by Doering and Gadoua by…

Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the…

Risk sensitive decision making finds important applications in current day use cases. Existing risk measures consider a single or finite collection of random variables, which do not account for the asymptotic behaviour of underlying…

We establish an exact asymptotic formula for the square variation of certain partial sum processes. Let $\{X_{i}\}$ be a sequence of independent, identically distributed mean zero random variables with finite variance $\sigma$ and…

This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…

In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…

In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…

This paper studies the fundamental limits of the minimum average length of lossless and lossy variable-length compression, allowing a nonzero error probability $\epsilon$, for lossless compression. We give non-asymptotic bounds on the…

We show an invariance principle for rescaled clocks of positive semi-stable Markov processes, proving a conjecture presented in Remark 4 in Demni, Rouault, Zani [11], 2015.

A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…

We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables like current and activity pertain to the first class, which is composed by random variables that change whenever a jump in…

Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…

The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their…

We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.

We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…

This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…

The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale.…

We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L^2 norms. The estimates in total…