Moment convergence of first-passage times in renewal theory

First Passage times in Biology: Approximations

Mean first-passage times for an ac-driven magnetic moment of a nanoparticle

– The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly rotating in the plane perpendicular to the easy axis of the nanoparticle governs the MFPTs just in the same way as a static magnetic field that is applied al...

First-passage times of regime switching models

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is – up to the roots of a polynomial of degree 4 (respectively 6) – deri...

Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment

We present an analytical method of calculating the mean first-passage times MFPTs for the magnetic moment of a uniaxial nanoparticle which is driven by a rapidly rotating, circularly polarized magnetic field and interacts with a heat bath. The method is based on the solution of the equation for the MFPT derived from the two-dimensional backward Fokker-Planck equation in the rotating frame. We s...

On the concentration and the convergence rate with a moment condition in first passage percolation

We consider the first passage percolation model on the Zd lattice. In this model, we assign independently to each edge e a non-negative passage time t(e) with a common distribution F . Let a0,n be the passage time from the origin to (n, 0, · · · , 0). Under the exponential tail assumption, Kesten (1993) and Talagrand (1995) investigated the concentration of a0,n from its mean using different me...