Related papers: Hitting Time Distributions for Denumerable Birth a…
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…
This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic…
We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give…
For the continuous-time $\lambda$-recurrent jump process, the $\lambda$-recurrence assures the existence of quasi-stationary distribution when it has finite exit states (the states that have positive killing rates). And we give an explicit…
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…
We investigate free-energy dissipation in a continuous-time birth-and-death dynamics in $\mathbb{R}^d$. For these Markov processes, the class of reversible measures coincides with the infinite-volume Gibbs point processes for some…
A novel approach is employed and developed to derive transition probabilities for a simple time-inhomogeneous birth-death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases.…
We study the Unitary Hitting Time Problem (UHTP) in quantum dynamics. Given computably described pure states |a>, |b> and a time-dependent unitary U(t), define the hitting time as the infimum of t > 0 such that the fidelity between U(t)|a>…
Haydn, Lacroix and Vaienti [Ann. Probab. 33 (2005)] proved that, for a given ergodic map, the entry time distribution converges in the small target limit, if and only if the corresponding return time distribution converges. The present note…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
This paper extends a recent extreme value law for horocycle flows on the space of two-dimensional lattices, due to Kirsebom and Mallahi-Karai, to the simplest examples of rank-$k$ unipotent actions on the space of $n$-dimensional lattices.…
In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ and obtain the asymptotic form of the…
This paper studies the quasi-stationary distributions for a single death process (or downwardly skip-free process) with killing defined on the non-negative integers, corresponding to a non-conservative transition rate matrix. The set…
The intensity of a Gibbs point process is usually an intractable function of the model parameters. For repulsive pairwise interaction point processes, this intensity can be expressed as the Laplace transform of some particular function.…
S. G. Kou and H. Wang [First Passage times of a Jump Diffusion Process \textit{Ann. Appl. Probab.} {\bf 35} (2003) 504--531] give expressions of both the (real) Laplace transform of the distribution of first passage time and the (real)…
We consider the first exit time of a Shiryaev-Roberts diffusion with constant positive drift from the interval $[0,A]$ where $A>0$. We show that the moment generating function (Laplace transform) of a suitably standardized version of the…
We study a continuous-time branching random walk on the lattice $\mathbb{Z}^{d}$, $d\in \mathbb{N}$, with a single source of branching, that is the lattice point where the birth and death of particles can occur. The random walk is assumed…
We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a…
We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace…
In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of "strong metastability time" is introduced to…