The asymptotic behaviour of probabilities of small deviations has been investigated for various classes of stochastic processes. Asymptotics of probabilities of small deviations for sums of independent random variables and homogeneous processes with independent increments were found in Mogul’skii [1], Borovkov and Mogul’skii [2] and references therein. Note that the last class of processes incl...

Suppose we have a renewal process observed over a fixed length of time starting from a random time point and only the times of renewals that occur within the observation window are recorded. Assuming a parametric model for the renewal time distribution with parameter θ , we obtain the likelihood of the observed data and describe the exact and asymptotic behavior of the Fisher information (FI) o...

An important characteristic of the grenewal process, and of great practical interest, is the grenewal equation, which represents the expected cumulative number of recurrent events as a function of time. The problem is that the grenewal equation does not have a closed form solution, unless the underlying event times are exponentially distributed. The Monte Carlo solution [10], although exhaus...

Urban renewal and sustainable development are two popular issues in both policy agenda and academia. Although their importance has been increasingly recognized, an integrated review covering sustainability, planning, and urban renewal has yet to be produced. Based on 81 journal papers, this paper presents a critical review of recent studies on sustainable urban renewal over the period 1990 to 2...

In the terms of operational calculus the probability characteristics of direct and reverse residual renewal time of alternating renewal process, where renewal time depends on life-time, are found. 1. Definitions, Motivations and Formulation of the Problem 1.1 According to [1] let’s consider a system which fails after random life-time X1 and is fully renewed after the lapse of random time Y1. Th...

This paper introduces a simple index that helps to assess the degree of aging or rejuvenation of repairable systems. The index ranges from -1 to 1. It is negative for the point processes with decreasing ROCOF and is positive for the point processes with increasing ROCOF. Index Terms aging, rejuvenation, homogeneity, non-homogeneity. ACRONYMS CDF cumulative distribution function CIF cumulative i...