Related papers: Asymptotic Mean Time To Failure and Higher Moments…
We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$…
We study large deviation asymptotics for processes defined in terms of continued fraction digits. We use the continued fraction digit sum process to define a stopping time and derive a joint large deviation asymptotic for the upper and…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Probabilistic model-based diagnosis computes the posterior probabilities of failure of components from the prior probabilities of component failure and observations of system behavior. One problem with this method is that such priors are…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
We consider a class of doubly weighted rank-based estimating methods for the transformation (or accelerated failure time) model with missing data as arise, for example, in case-cohort studies. The weights considered may not be predictable…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
Consider a sequence of continuous-time Markov chains $(X^{(n)}_t:t\ge 0)$ evolving on a fixed finite state space $V$. Let $I_n$ be the level two large deviations rate functional for $X^{(n)}_t$, as $t\to\infty$. Under a hypothesis on the…
Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent…
The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…
The article is focused on studying how to predict the failure times of coherent systems from the early failure times of their components. Both the cases of independent and dependent components are considered by assuming that they are…
Reliability in multi-agent systems (MAS) built on large language models is increasingly limited by cognitive failures rather than infrastructure faults. Existing observability tools describe failures but do not quantify how quickly…
Ability to count number of occurrences of events within a specified time interval is very useful in specification of resource bounded real time computation. In this paper, we study an extension of Metric Temporal Logic ($\mathsf{MTL}$) with…
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns…
Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these…
We study systems of nonlinear ordinary differential equations where the dominant term, with respect to large spatial variables, causes blow-ups and is positively homogeneous of a degree $1+\alpha$ for some $\alpha>0$. We prove that the…
In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization…
This paper delves into a comprehensive analysis of fault-tolerant memory systems, focusing on recovery techniques modeled using Markov chains to address transient errors. The study revolves around the application of scrubbing methods in…