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Milto Hadjikyriakou

Publications and source records attributed to Milto Hadjikyriakou.

15 recordsLinked to original sources
arXiv2026

Doob-type optional sampling theorems for demimartingales with applications to associated sequences

We establish optional sampling inequalities for demimartingales and demisubmartingales under suitable monotonicity assumptions on the stopping rule. First, we establish comparison inequalities for processes stopped at bounded stopping times and identify broad classes of threshold-type stopping times for which the required assumptions are naturally satisfied. We then prove Doob-type optional sampling inequalities for possibly unbounded stopping times under standard integrability conditions. As applications, we derive maximal inequalities for demi(sub)martingales, obtain an almost sure bound for the maximal negative excursion of partial sums of positively associated random variables, and establish generalized Wald-type inequalities, including nonlinear convex-transform inequalities for associated sequences.

math.PR↗
arXiv2026

Stochastic Ordering of Dependent Systems under Transformation Models and Archimedean Copulas

We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean copulas, allowing for a unified treatment of several transformation-based models, including proportional hazard, proportional reversed hazard rate and proportional odds families. For parallel, series and $(n-k)$-out-of-$n$ systems, we derive conditions for stochastic dominance based on monotonicity of the transformation and structural properties of the copula generators, formulated through super-additivity and Schur-type arguments. The results provide tractable criteria that extend existing comparisons beyond independence and illustrate the combined effect of dependence and parameter heterogeneity on system reliability.

math.PR↗
arXiv2025

Stochastic orders and shape properties for a new distorted proportional odds model

Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying baseline distribution. The first model offers enhanced control over odds and log-odds functions, facilitating adjustments to skewness, tail behaviour, and hazard rates. The second model, with even greater flexibility, describes odds ratios as quantile distortions. This approach leads to an enlarged log-logistic family capable of capturing these quantile transformations and diverse hazard behaviours, including non-monotonic and bathtub-shaped rates. Central to our study are the shape relations described through stochastic orders; we establish conditions that ensure stochastic ordering both within each family and across models under various ordering concepts, such as hazard rate, likelihood ratio, and convex transform orders

math.ST↗
arXiv2024

On the limit distribution of extremes of generalized Oppenheim random variables

This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim expansions belong to the maximum domain of attraction of the Frechet distribution. Additionally, we identify conditions under which the maxima and minima of Oppenheim random variables demonstrate some kind of asymptotic independence. Finally, we prove an Extreme Types theorem for Oppenheim expansions with unknown dependent structure.

math.PR↗
arXiv2023

Strong laws of large numbers for lightly trimmed sums of generalized Oppenheim expansions

In the framework of generalized Oppenheim expansions we prove strong law of large numbers for lightly trimmed sums. In the first part of this work we identify a particular class of expansions for which we provide a convergence result assuming that only the largest summand is deleted from the sum; this result generalizes a strong law recently proven for the Luroth case. In the second part we drop any assumptions concerning the structure of the Oppenheim expansions and we prove a result concerning trimmed sums when at least two summands are trimmed; then we derive a corollary for the case in which only the largest summand is deleted from the sum.

math.PR↗
arXiv2023

Intermediately Trimmed Sums of Oppenheim Expansions: a Strong Law

The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not identically distributed random variables converge almost surely. Moreover, by dropping the assumption of independence we provide a corresponding convergence result for a special class of Oppenheim expansions. We highlight that the results of this paper generalize the results provided in the recent work of \cite{KS} while the convergence of intermediately trimmed sums of generalized Oppenheim expansions is studied for the first time.

math.PR↗
arXiv2023

Discrete Gronwall inequalities for demimartingales

The aim of this work is to obtain discrete versions of stochastic Gronwall inequalities involving demimartingale sequences. The results generalize the respective theorems for martingales provided by Kruse and Scheutzow (2018) and Hendy et al. (2022). Moreover, we present an application which provides an upper bound for the a priori estimate of the backward Euler-Maruyama numerical scheme.

math.PR↗
arXiv2022

Maximal inequalities and convergence results on multidimensionally indexed demimartingales

We obtain some maximal probability and moment inequalities for multidimensionally indexed demimartingales. Although the class of single-indexed demimartingales has been studied extensively, no significant amount of work has been done for the corresponding multiindexed class of random variables. This work aims to fill in this gap in the literature by extending well-known inequalities and asymptotic results to this more general class of random variables.

math.PR↗
arXiv2022

New asymptotic results for generalized Oppenheim expansions

In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables under study have infinite mean and the results are obtained without any dependence assumptions.

math.PR↗
arXiv2020

Convergence for weighted sums of Luroth type random variables

In this work we prove an asymptotic result, that under some conditions on the involved distribution functions, is valid for any Oppenheim expansion, extending a classical result proven by W. Vervaat in 1972 for denominators of the Luroth case. Furthermore, we study the convergence in distribution of weighted sums of a sequence of independent random variables. Although the result is of its own interest, in the present setting it is used to prove convergence in distribution of specific sequences of random variables generalizing known results obtained for Luroth random variables.

math.PR↗
arXiv2020

On exact laws of large numbers for Oppenheim expansions with infinite mean

In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions. More precisely, we verify convergence in probability as well as almost sure convergence to a strictly positive and finite constant without assuming any dependence structure or the existence of means. Results of this kind are known as exact weak and exact strong laws.

math.PR↗
arXiv2019

Non-comparability with respect to the convex transform order with applications

In the literature of stochastic orders, one rarely finds results that can be considered as criteria for the non-comparability of random variables. In this paper, we provide results that enable researchers to use simple tools to conclude that two random variables are not comparable with respect to the convex transform order. The criteria are applied to prove the non-comparability of parallel systems with components that are either exponential, Weibull or Gamma distributed, providing a negative answer for a conjecture about comparability with respect to the convex transform order in a much broader scope than its initial statement.

math.PR↗
arXiv2019

On the limit behavior of iterated equilibrium distributions for the Gamma and Weibull families

In this paper, we study the evolution of iterated equilibrium distributions for the Gamma and Weibull families of distributions as the iteration step increases. We characterize their moments and the pointwise limit of the distribution functions corresponding to the iterated distributions. As a byproduct, we obtain approximations for higher order moments of the residual lifetime.

math.ST↗
arXiv2018

Failure Rate Properties of Parallel Systems

We study failure rate monotonicity and generalized convex transform stochastic ordering properties of random variables, with a concern on applications. We are especially interested in the effect of a tail weight iteration procedure to define distributions, which is equivalent to the characterization of moments of the residual lifetime at a given instant. For the monotonicity properties, we are mainly concerned with hereditary properties with respect to the iteration procedure providing counter-examples showing either that the hereditary property does not hold or that inverse implications are not true. For the stochastic ordering, we introduce a new criterium, based on the analysis of the sign variation of a suitable function. This criterium is then applied to prove ageing properties of parallel systems formed with components that have exponentially distributed lifetimes.

math.PR↗