Related papers: Strong times and first hitting

We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as…

A new stochastic process is introduced and considered - squared Bessel process with special stochastic time. The analogues of fundamental properties for Brownian motion are deduced for squared Bessel process. In particular an analogue of…

In this paper we propose the method to find the hitting probabilities for Gaussian integrators. Using second quantization we obtain the sseries representation for such probabilities despite the fact that integrators can be non-Markov…

In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study…

The mean time taken by an irreducible Markov chain on a finite state space to hit a target chosen at random according to the stationary distribution does not depend on the initial state of the chain. This mean time is known as Kemeny's…

We study the time reversal of a general PDMP. The time reversed process is defined as $X_{(T-t)-}$, where $T$ is some given time and $X_t$ is a stationary PDMP. We obtain the parameters of the reversed process, like the jump intensity and…

We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…

Stochastic time-varying optimization is an integral part of learning in which the shape of the function changes over time in a non-deterministic manner. This paper considers multiple models of stochastic time variation and analyzes the…

We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the…

We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval $[0,A]$ as $A\to\infty$. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably…

For one-dimensional symmetric L\'{e}vy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is either a single point or an interval. The estimates are…

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…

We show that the generation time -- a notion usually described in a biological context -- can be defined in a general way as a return time in a conveniently constructed finite Markov chain. The simple formula we obtain agrees with previous…

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…

Consider a sequence of continuous-time irreducible reversible Markov chains and a sequence of initial distributions, $\mu_n$. The sequence is said to exhibit $\mu_n$-cutoff if the convergence to stationarity in total variation distance is…

We consider a random walk on a discrete connected graph having some infinite branches plus finitely many vertices with finite degrees. We find the generator of a strong stationary dual in the sense of Fill, and use it to find some…

The distribution of the "mixing time" or the "time to stationarity" in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the…

The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…

We consider reversible ergodic Markov chains with finite state space, and we introduce a new notion of quasi-stationary distribution that does not require the presence of any absorbing state. In our setting, the hitting time of the…

We prove that the class of discrete time stationary max-stable process satisfying the Markov property is equal, up to time reversal, to the class of stationary max-autoregressive processes of order $1$. A similar statement is also proved…