相关论文: Invertibility of functionals of the Poisson proces…

Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, where exogenously generated initial events give rise to endogenously driven descendant events. This perspective provides…

We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…

In the paper we study the models of time-changed Poisson and Skellam-type processes, where the role of time is played by compound Poisson-Gamma subordinators and their inverse (or first passage time) processes. We obtain explicitly the…

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…

The problem of characterizing all new-time transformations preserving the Poisson structure of a finitedimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously…

Several stochastic processes related to transient L\'evy processes with potential densities $u(x,y)=u(y-x)$, that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of…

The role of time reversal invariance in the phenomenology of transverse spin is discussed.

In this article, we introduce fractional Poisson felds of order k in n-dimensional Euclidean space $R_n^+$. We also work on time-fractional Poisson process of order k, space-fractional Poisson process of order k and tempered version of…

We review the behaviour of the Gibbs' and conditional entropies in deterministic and stochastic systems and continue to a formulation appropriate for a stochastically perturbed system with delayed dynamics. The underlying question driving…

We consider the infinite divisibility of distributions of some well-known inverse subordinators. Using a tail probability bound, we establish that distributions of many of the inverse subordinators used in the literature are not infinitely…

All of the basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system…

Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes.…

We study the impact of the recently introduced underspread/overspread classificationon the spectra of processes with square-integrable covariance functions. We briefly review the most prominent definitions of a time-varying power spectrum…

The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition…

In the macroscopic world, time is intrinsically asymmetric, flowing in a specific direction, from past to future. However, the same is not necessarily true for quantum systems, as some quantum processes produce valid quantum evolutions…

Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…

I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst"…

In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time…