Related papers: Characteristics of the switch process and geometri…
As a follow-up to a recent paper considering two symmetric queues, the \textit{Shortest Queue First} service discipline is presently analysed for two general asymmetric queues. Using the results previously established and assuming…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other…
We consider a stochastic process undergoing resetting after which a random refractory period is imposed. In this period the process is quiescent and remains at the resetting position. Using a first-renewal approach, we compute exactly the…
Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
In one-dimensional random walks, the waiting time for each direction transitions is the same, even in the presence of bias, as a consequence of the microscopic-reversibility. We study the symmetry breaking of forward/ backward transition…
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…
A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with…
We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit…
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a L\'{e}vy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent L\'{e}vy measure, local…
Transition probabilities for stochastic systems can be expressed in terms of a functional integral over paths taken by the system. Evaluating the integral by the saddle point method in the weak-noise limit leads to a remarkable mapping…
As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…