Strong convergence of a positive preserving drift-implicit Euler scheme for the fixed delay CIR process

In this paper, we consider a fixed delay Cox-Ingersoll-Ross process (CIR process) on the regime where it does not hit zero, the aim is to determine a positive preserving implicit Euler Scheme. On a time grid with constant stepsize our scheme extends the scheme proposed by Alfonsi in 2005 for the classical CIR model. Furthermore, we consider its piecewise linear interpolation, and, under suitable conditions, we establish the order of strong convergence in the uniform norm, thus extending the results of Dereich et al. in 2011.Comment: 24 page

Revisiting Relations between Stochastic Ageing and Dependence for Exchangeable Lifetimes with an Extension for the IFRA/DFRA Property

We first review an approach that had been developed in the past years to introduce concepts of "bivariate ageing" for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate ageing. A specific feature of such an approach dwells on the concept of semi-copula and in the extension, from copulas to semi-copulas, of properties of stochastic dependence. In this perspective, we aim to discuss some intricate aspects of conceptual character and to provide the readers with pertinent remarks from a Bayesian Statistics standpoint. In particular we will discuss the role of extensions of dependence properties. "Archimedean" models have an important role in the present framework. In the second part of the paper, the definitions of Kendall distribution and of Kendall equivalence classes will be extended to semi-copulas and related properties will be analyzed. On such a basis, we will consider the notion of "Pseudo-Archimedean" models and extend to them the analysis of the relations between the ageing notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD

Nonlinear filtering for Markov systems with delayed observations

Versione iniziale di un lavoro successivamente pubblicato (altra versione disponible su) http://www.mat.uniroma1.it/people/nappo/papers.pdf/CFN-JAMCS-DelayMarkov.pd

Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes

As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables $T_{1},...,T_{r}$. In any case, we assume that $T_{1},...,T_{r}$ are identically distributed, with a common survival function $\overline{G}$ and their survival copula is denoted by $K$. The diagonal's and subdiagonals' sections of $K$, along with $\overline{G}$, are possible tools to describe the information needed to recover the laws of order statistics. When attention is restricted to the absolutely continuous case, such a joint distribution can be described in terms of the associated multivariate conditional hazard rate (m.c.h.r.) functions. We then study the distributions of the order statistics of $T_{1},...,T_{r}$ also in terms of the system of the m.c.h.r. functions. We compare and, in a sense, we combine the two different approaches in order to obtain different detailed formulas and to analyze some probabilistic aspects for the distributions of interest. This study also leads us to compare the two cases of exchangeable and minimally stable variables both in terms of copulas and of m.c.h.r. functions. The paper concludes with the analysis of two remarkable special cases of stochastic dependence, namely Archimedean copulas and load sharing models. This analysis will allow us to provide some illustrative examples, and some discussion about peculiar aspects of our results

Continuous time random walks and queues: explicit forms and approximations of the conditional law with respect to local times

Abstract In the filtering problem considered here, the state process is a continuous time random walk and the observation process is an increasing process depending deterministically on the trajectory of the state process. An explicit construction of the filter is given. This construction is then applied to a suitable approximation of a Brownian motion and to a rescaled M/M/1 queueing model. In both these cases, the sequence of the observation processes converges to a local time, and a convergence result for the respective filters is given. The case of a queueing model when the observation is the idle time is also considered

The filtered martingale problem

Abstract Let X be a Markov process characterized as the solution of a martingale problem with generator A, and let Y be a related observation process. The conditional distribution π t of X(t) given observations of Y up to time t satisfies certain martingale properties, and it is shown that any probability-measure-valued process with the appropriate martingale properties can be interpreted as the conditional distribution of X for some observation process. In particular, if Y (t) = γ(X(t)) for some measurable mapping γ, the conditional distribution of X(t) given observations of Y up to time t is characterized as the solution of a filtered martingale problem. Uniqueness for the original martingale problem implies uniqueness for the filtered martingale problem which in turn implies the Markov property for the conditional distribution considered as a probability-measure-valued process. Other applications include a Markov mapping theorem and uniqueness for filtering equations. MSC 2000 subject classifications: 60J25, 93E11, 60G35, 60J35, 60G4

Inhibition of the glucocorticoid receptor results in an enhanced miR-99a/100-mediated radiation response in stem-like cells from human prostate cancers

Radiation therapy is a major primary treatment option for both localized early stage prostate cancer, and for advanced, regionally un-resectable, cancer. However, around 30% of patients still experience biochemical recurrence after radiation therapy within 10 years. Thus, identification of better biomarkers and new targets are urgently required to improve current therapeutic strategies. The miR-99 family has been shown to play an important role in the regulation of the DNA damage response, via targeting of the SWI/SNF chromatin remodeling factors, SMARCA5 and SMARCD1 in cell line models. In the present study, we have demonstrated that low expression of miR-99a and miR-100 is present in cell populations which are relatively radiation insensitive, for example in prostate cancer stem cells and in castration-resistant prostate cancer. Additionally, treatment of cells with the synthetic glucocorticoid, Dexamethasone resulted in decreased miR-99a and 100 expression, suggesting a new mechanism of miR-99a and 100 regulation in androgen-independent prostate cells. Strikingly, treatment of prostate cells with the glucocorticoid receptor inhibitor, Mifepristone was found to sensitize prostate cells to radiation by increasing the levels of miR-99a and miR-100. These results qualify the miR99 family as markers of radiation sensitivity and as potential therapeutic targets to improve efficiency of radiotherapy