Appendix A. There exists a Cox process with an a.s. C ∞ intensity coinciding with any finite dimensional prior. In this section we prove the proposition below. Proposition .1 Let Q be an (n + 1) dimensional continuous probability distribution whose density has support n+1 i=1 ]0, +∞[, and let x 1 ,. .. , x n be n points on a compact domain S ⊂ R d. There exists an almost surely non-negative and...

The model introduced in this article is designed to provide a consistent representation for both the real-world and pricing measures for the credit process. We find that good agreement with historical and market data can be achieved across all credit ratings simultaneously. The model is characterized by an underlying stochastic process that takes on values on a discrete lattice and represents c...

We investigate the asymptotic properties of the maximum likelihhod estimator and Bayes estimator of the drift parameter for stochastic processes satisfying a linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

In Dekel and Feinberg (2004) we suggested a test for discovering whether a potential expert is informed of the distribution of a stochastic process. This category test requires predicting a “small”– category I – set of outcomes. In this paper we show that there is a randomized category test that cannot be manipulated, i.e. such that no matter how the potential expert randomizes his prediction, ...

Over the last two decades, there has been an increasing awareness of, and interest in, the use of spatial moment techniques to provide insight into a range of biological and ecological processes. Models that incorporate spatial moments can be viewed as extensions of mean-field models. These mean-field models often consist of systems of classical ordinary differential equations and partial diffe...

Given a stochastic process Xt, t b T CR, and s ~ R, then a) iff b): a) For every probability measure p on there is a stopping time T for Xt with law L(T) = p: b) If At is the smallest a-algebra for which Xu are measurable for all u ~ t, then P restricted to At is nonatomic for all t > s. This note began with a question of G. Shiryaev, connected with the following example. Let Wt be a standard W...

For a class of fast Cl-type inhibitory spiking neuron models with delayed feedback fed with a Poisson stochastic process of excitatory impulses, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order.

1. Discrete-Event Stochastic Systems Recall our previous definition of a discrete-event stochastic system: the system makes stochastic state transitions only at an increasing sequence of random times. If X(t) is the state of the system at time t, then a typical sample path of the underlying stochastic process of the simulation, i.e. (X(t): t ≥ 0), looks like this (for a finite or countably infi...

The use of reduced basis has spread to many scientific fields for the last fifty years to condense the statistical properties of stochastic processes. Among these basis, the classical Karhunen-Loève basis corresponds to the Hilbertian basis that is constructed as the eigenfunctions of the covariance operator of the stochastic process of interest. The importance of this basis stems from its opti...