We propose a unified quasi-likelihood procedure for the estimation of the unknown parameters of a first-order random coefficient autoregressive, RCA, model that works both for stationary and nonstationary processes. For this procedure, the weak consistency and the asymptotic normality are established under minimal assumptions on the noise sequences. In an empirical study, we highlight the pract...

A classification method based on textural information for metallic surfaces displaying complex random patterns is proposed. Because these kinds of textures show fluctuations at a small scale and some uniformity at a larger scale, a probabilistic approach is followed, considering textural variations as realizations of random functions. Taking into account information of pixel neighbourhoods, the...

A zero-knowledge authentication scheme is a type of authentication scheme, which gives no knowledge beyond the authenticity identifying an entity and is probabilistic than deterministic authentication scheme. This paper proposes Diffie-Hellman and Fiat-Shamir like zero-knowledge authentication schemes on general non-commutative groups. The key idea of our proposal is that for a given non-commut...

The choice of a reference image typically influences the results of deformable image registration, thereby making it asymmetric. This is a consequence of a spatially non-uniform weighting in the cost function integral that leads to general registration inaccuracy. The inhomogeneous integral measure--which is the local volume change in the transformation, thus varying through the course of the r...

Through the use of a few examples, we shall illustrate the use of probability theory, or otherwise, in the study of upper bound questions in the theory of irregularities of point distribution. Such uses may be Monte Carlo in nature but the most efficient ones appear to be quasi Monte Carlo in nature. Furthermore, we shall compare the relative merits of probabilistic and non-probabilistic techni...

This thesis deals with the fully automatic generation of semantic annotations for medical imaging data by means of medical image segmentation and labeling. In particular, we focus on the segmentation of the human brain and related structures from magnetic resonance imaging (MRI) data. We present three novel probabilistic methods from the field of database-guided knowledge-based medical image se...

Many practical control problems are so complex that traditional analysis and design methods fail to solve. Consequently, in recent years probabilistic methods that provide approximate solutions to such ’difficult’ problems have emerged. Unfortunately, the uniform random sampling process usually used in such techniques unavoidably leads to clustering of the sampled points in higher dimensions. I...

The subject of this paper is a fragmentation equation with non-conservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the fragmentation rate, we describe the largetime behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equation ar...

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward–backward stochastic differential equations and introduce the new concept of " auxiliary SDEs. " 1. Introduction and assumptions.

We prove a general finite-time convergence theorem for fixpoint expressions over a well-quasi-ordered set. This has immediate applications for the verification of well-structured systems, where a main issue is the computability of fixpoint expressions, and in particular for game-theoretical properties and probabilistic systems where nesting and alternation of least and greatest fixpoints are co...