Related papers: On functional records and champions
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Given a sequence of independent random vectors taking values in ${\mathbb R}^d$ and having common continuous distribution function $F$, say that the $n^{\rm \scriptsize th}$ observation sets a (Pareto) record if it is not dominated (in…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
The sequence of so-called signature moments describes the laws of many stochastic processes in analogy with how the sequence of moments describes the laws of vector-valued random variables. However, even for vector-valued random variables,…
Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…
We propose a notion of iterating functions $f:X^{k}\rightarrow X$ in a way that represents recurrence relations of the form $a_{n+k}=f(a_{n},a_{n+1},...,a_{n+k-1})$. We define a function as $n$-involutory when its $n$th iterate is the…
Combining data from various sources empowers researchers to explore innovative questions, for example those raised by conducting healthcare monitoring studies. However, the lack of a unique identifier often poses challenges. Record linkage…
Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not even be an option. In this paper, we give…
Let X_1,...., X_n be a collection of iid discrete random variables, and Y_1,..., Y_m a set of noisy observations of such variables. Assume each observation Y_a to be a random function of some a random subset of the X_i's, and consider the…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given \xi_i > 0. This problem, with random…
We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the…
In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X =^d…
We consider the best-choice problem for independent (not necessarily iid) observations $X_1, \cdots, X_n$ with the aim of selecting the sample minimum. We show that in this full generality the monotone case of optimal stopping holds and the…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random…
Iteration of randomly chosen quadratic maps defines a Markov process: X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with values in the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta x(1-x). Its study is of…
Various kinds of uncertainty can occur in event logs, e.g., due to flawed recording, data quality issues, or the use of probabilistic models for activity recognition. Stochastically known event logs make these uncertainties transparent by…