Should recombinations of radical pairs be considered as accompanied by measurements?

The so-called "phenomenological" kinetic equation for one-pair density operator for spin-selective reactions is defended. We derive this equation from the kinetic equation for density operator of all pairs which are treated as singlet and triplet bosons. There presented some reasons for inconsistency of measurement-like approach to the problem.Comment: 6 page

On limiting cluster size distributions for processes of exceedances for stationary sequences

It is well known that, under broad assumptions, the time-scaled point process of exceedances of a high level by a stationary sequence converges to a compound Poisson process as the level grows. The purpose of this note is to demonstrate that, for any given distribution G on the natural numbers, there exists a stationary sequence for which the compounding law of this limiting process of exceedances will coincide with G.Comment: 6 pages, no figure

On exit times of Levy-driven Ornstein--Uhlenbeck processes

We prove two martingale identities which involve exit times of Levy-driven Ornstein--Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption that positive jumps of the Levy process are exponentially distributed.Comment: 12 page

On approximation rates for boundary crossing probabilities for the multivariate Brownian motion process

Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with respect to small changes of the boundary. Under broad assumptions on the nature of the boundary, including the Lipschitz condition (in a Hausdorff-type metric) on its time cross-sections, we obtain an analogue of the Borovkov and Novikov (2005) upper bound for the difference between boundary hitting probabilities for "close boundaries" in the univariate case. We also obtained upper bounds for the first boundary crossing time densities.Comment: 15 page