Related papers: Concentration Inequalities for Markov Jump Process…

We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…

Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…

While classical concentration inequalities are typically restricted to two special cases -- independence and martingale difference sequences -- we extend concentration inequalities to a much broader class of stochastic processes by relaxing…

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…

We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…

We prove a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. Working with bounded and $\pi$-canonical kernels, we show that we can recover the convergence rate of Arcones and Gin{\'e} who proved…

In this study, we address the central issue of statistical inference for Markov jump processes using discrete time observations. The primary problem at hand is to accurately estimate the infinitesimal generator of a Markov jump process, a…

The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…

We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a…

In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for discrete-time matrix local martingales,…

We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use…

Let $\{W_t\}_{t=1}^{\infty}$ be a finite state stationary Markov chain, and suppose that $f$ is a real-valued function on the state space. If $f$ is bounded, then Gillman's expander Chernoff bound (1993) provides concentration estimates for…

We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the…

We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various…

We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds…

We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…

For a wide class of monotonic functions $f$, we develop a Chernoff-style concentration inequality for quadratic forms $Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2$, where $Z_i \sim N(0,1)$. The inequality is expressed in terms…