相关论文: Rice Formula for processes with jumps and applicat…

By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…

In this note we show a simple formula for the joint density of local times, last exit tree and cycling numbers of continuous-time Markov Chains on finite graphs, which involves the modified Bessel function of the first type.

We review the properties of time intervals between the crossings at a level M of a smooth stationary Gaussian temporal signal. The distribution of these intervals and the persistence are derived within the Independent Interval Approximation…

We derive explicit formulas for probabilities of Brownian motion with jumps crossing linear or piecewise linear boundaries in any finite interval. We then use these formulas to approximate the boundary crossing probabilities for general…

The paper examines a class of first order linear hyperbolic systems, proposed as a generalization of the Goldstein-Kac model for velocity-jump processes and determined by a finite number of speeds and corresponding transition rates. It is…

In this paper, we discuss general criteria of limsup law of iterated logarithm (LIL) for continuous-time Markov processes. We consider minimal assumptions for LILs to hold at zero(at infinity, respectively) in general metric measure spaces.…

Understanding the statistics of level crossings in stochastic processes is crucial across many scientific disciplines. The traditional Kac-Rice formula gives the mean rate of level crossings and has found broad use. However, that mean rate…

A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…

We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…

In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the…

This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a…

A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…

This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However, it still enjoys the interesting properties of a reciprocal…

We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…

We introduce the concept of `discrete-time persistence', which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n \Delta T. For a Gaussian Markov process with relaxation rate \mu, we show…

Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…