Quasi-product forms for L

We study stochastic tree fluid networks driven by a multidimensional

Extremes of multidimensional Gaussian processes

This paper considers extreme values attained by a centered, multidimensional Gaussian process t) = (X_1(t), ..., X_n(t)) minus drift d(t) = (d_1(t), ..., d_n(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of the logarithm of the probability that for some t in T, we have that (for all i = 1, ..., n) X_i(t) - d_i(t) > q_i u, for positive thresholds q_i > 0 and u large. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional case. A number of examples illustrate the theory

Logarithmic Asymptotics For Probability Of Component-Wise Ruin In A Two-Dimensional Brownian Model

We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function P(u) for the component-wise ruin (that is both business lines are ruined in an infinite-time horizon), where u is the same initial capital for each line. We measure the goodness of the business by analysing the adjustment coefficient, that is the limit of − ln P(u)/u as u tends to infinity, which depends essentially on the correlation ρ of the two surplus processes. In order to work out the adjustment coefficient we solve a two-layer optimization problem

Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Endocrine therapy in epithelial ovarian cancer

INTRODUCTION: The estrogen receptor (ER) is expressed at high levels in many epithelial ovarian cancers (EOC) and represents a potential target for endocrine therapy. Both anti-estrogens and aromatase inhibitors have been evaluated in phase II clinical trials. Areas covered: We present an overview of the phase II and phase III trials of anti-estrogens (tamoxifen and fulvestrant) and aromatase inhibitors (letrozole, anastrazole and exemestane) undertaken in epithelial ovarian cancer identified through a Pubmed search. We describe predictive biomarkers that are being investigated to identify responsive cancers. Expert commentary: The efficacy of endocrine therapy in epithelial ovarian cancer is likely to be confined to histological subtypes with the highest ER expression while low grade serous ovarian cancer appears to be one subgroup with good sensitivity to these agents. The low toxicity profile of these agents is favourable although their use is unlicensed and the optimal setting undefined. Prospective clinical trials of endocrine agents in the early relapse and maintenance settings are urgently required to establish their definitive role in the management of epithelial ovarian cancer