We solve a natural inverse problem for transition probabilities for Markov chains on rooted trees using hitting time distribution for leaves. Our solution is algorithmic and the natural statistics associated to our algorithm are consistent.

We extend an old result by Doob characterizing real-valued, Gaussian, stationary, Markov processes to the vector case. In this case a deterministic component appears that consists of a system of harmonic oscillators while the random part is a collection of independent oscillator processes,...

Previous work of J.T. Lewis is extended to include diffusions on level sets of functions [phi]n-->k with n >k in terms of the coordinates of the host space. The particular case k = 1 extends previous related work of M. van den Berg and J.T. Lewis.

Purpose: This paper aims to illustrate, within the context of a well-known linear diversification model, that risk management as exerted by banks and regulators ultimately depends on how risk is assessed and conceptualized. The two risk metrics used are the probability of bank failure and value...