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According to the Ray-Knight description, the Brownian local time in some conditional probability space is a diffusion process with respect to spatial variable. This diffusion has a local time. Thus the following definition of local time of the original Brownian local time seems to be natural: such a process is called the second-order Brownian local time. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order. [ABSTRACT FROM AUTHOR]

A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for unsupervised classification of asymmetric clusters in the presence of outliers and noise. A series of constraints are applied to a modified factor analyzer structure of the component scale matrices, yielding a family of twelve models. Application of the modified factor analyzer structure and these parsimonious constraints makes these models effective for the analysis of high-dimensional data by reducing the number of free parameters that need to be estimated. A variant of the expectation-maximization algorithm is developed for parameter estimation with convergence issues being discussed and addressed. Popular model selection criteria like the Bayesian information criterion and the integrated complete likelihood (ICL) are utilized, and a novel modification to the ICL is also considered. Through a series of simulation studies and real data analyses, that includes comparisons to well-established methods, we demonstrate the improvements in classification performance found using the proposed family of models. [ABSTRACT FROM AUTHOR]

We present a novel depth from focus technique. Following prior work, our pipeline starts with a focal stack and an estimation of the amount of defocus as given by, for instance, the ring difference filter. To improve robustness to outliers while avoiding to rely on costly nonlinear optimizations, we propose an original scheme that linearly scans the profile over a fixed size window, searching for the best peak within each window using a linearized least-squares Laplace regression. As a post-process, depth estimates with low confidence are reconstructed though an adaptive moving least squares filter. We show how to objectively evaluate the performance of our approach by generating synthetic focal stacks from which the reconstructed depth maps can be compared to ground truth. Our results show that our method achieves higher accuracy than previous nonlinear Laplace regression technique, while being orders of magnitude faster. [ABSTRACT FROM AUTHOR]

Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study cases where the autoregressive parameter is constant as well as a discrete or a continuous random variable. More general dependence structures are also discussed. Our primary aim is to investigate a broad class of recursions of autoregressive type for which several independence assumptions are lifted and for which a detailed exact analysis is provided. We provide expressions for the Laplace transform of the waiting time distribution of a customer in the system in terms of an infinite sum of products of known Laplace transforms. An integer-valued reflected autoregressive process that can be used to model a novel retrial queueing system with impatient customers and a general dependence structure is also considered. For such a model, we provide expressions for the probability generating function of the stationary orbit queue length distribution in terms of an infinite sum of products of known generating functions. A first attempt towards a multidimensional setting is also considered. [ABSTRACT FROM AUTHOR]