Related papers: Quasi-ergodic theorems for Feynman-Kac semigroups …
Continuous-time random walk (CTRW) is a model of anomalous sub-diffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, $\psi(\tau) \tau^{-(1+\alpha)}$, leads to…
The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…
A quasiclassical correspondent for the fermion degrees of freedom is obtained by using a time-dependent variational principle with Grassmann coherent states as trial functions. In the real parametrization provided by the canonical…
We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.
This paper presents the strong law of large numbers for a function of the local times of a transient random walk on groups, extending the research of Asymont and Korshunov for random walks on the integer lattice $\mathbb{Z}^d$. Under some…
We study large deviations principles for $ N $ random processes on the lattice $ \Z^d $ with finite time horizon $ [0,\beta] $ under a symmetrised measure where all initial and terminal points are uniformly given by a random permutation.…
In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
In this paper, we formulate and prove new properties of conditional quantiles given one of the particular sigma-fields. Next, we use them to investigate almost sure asymptotic behavior of central order statistics which arise from strictly…
In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+\alpha}$ diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property…
We generalize Anderson's orthogonality determinant formula to describe the statistics of work performed on generic disordered, non-interacting fermionic nanograins during quantum quenches. The energy absorbed increases linearly with time,…
We prove mean and pointwise ergodic theorems for general families of averages on a semisimple algebraic (or S-algebraic) group G, together with an explicit rate of convergence when the action has a spectral gap. Given any lattice in G, we…
In this chapter we present transformation semigroups and their applications. We begin with Klein's approach to geometry based on invariants of transformation groups. Then we present symmetry groups in chemistry and in classical mechanics.…
In the first part of this paper, we give a useful criterion for uniform integrability of exponential martingales in the context of Markov processes. The condition of this criterion is easy to verify and is, in general, much weaker than the…
We introduce a class of L\'{e}vy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions…
We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process…
We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space…
The well-known Jewett-Krieger's Theorem states that each ergodic system has a strictly ergodic model. Strengthening the model by requiring that it is strictly ergodic under some group actions, and building the connection of the new model…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
This paper deals with the ergodicity and the existence of a strong law of large numbers for adaptive Markov Chain Monte Carlo. We show that a diminishing adaptation assumption together with a drift condition for positive recurrence is…