Occupation time distributions for the telegraph process

On explicit occupation time distributions for Brownian processes

Explicit expressions for the occupation time distribution of Brownian bridge, excursion and meander are derived using Kac’s formula and results of [4]. The first two distributions appeared in [8], and were derived using weak convergence of simple random walk.

Quantitative estimates for the long time behavior of an ergodic variant of the telegraph process

Motivated by stability questions on piecewise deterministic Markov models of bacterial chemotaxis, we study the long time behavior of a variant of the classic telegraph process having a non-constant jump rate that induces a drift towards the origin. We compute its invariant law and show exponential ergodicity, obtaining a quantitative control of the total variation distance to equilibrium at ea...

On Parameter Estimation of Hidden Telegraph Process

The problem of parameter estimation is considered for the twostate telegraph process, observed in white Gaussian observation noise. An online one-step Maximum Likelihood Estimator (MLE) process is constructed, using a preliminary Method of Moments (MM) estimator. The obtained estimation procedure is shown to be asymptotically normal and efficient in the large sample regime. MSC 2000 Classificat...

Analytical Solution for the Time-Fractional Telegraph Equation

We discuss and derive the analytical solution for three basic problems of the so-called timefractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in...

The variational iteration method for solving Nagumo telegraph equation