General drawdown of general tax model in a time-homogeneous Markov framework

Drawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure), and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with more general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative Lévy processes [9, 20]. In this paper we further examine the general drawdown-related quantities in the (upward skip-free) time-homogeneous Markov process, and then in its (general) tax process by noticing the pathwise connection between general drawdown and the tax process.

SIMULATION AND CONTROL OF CLOSED-LOOP SYSTEMS WITH INTERNAL RESERVES

Рассматривается задача воспроизведения в искусственных объектах способности естественных систем к самовосстановлению вследствие существования в них замкнутого круговорота вещества и энергии. Показано, что создание замкнутого жизненного цикла в системе предполагает реализацию в ней процессов восстановления ресурсов и их накопления в виде внутренних резервов, расходуемых системой в неблагоприятных условиях существования. Получена функциональная схема системы с замкнутым циклом и предложена математическая модель её функционирования в виде дискретного однородного марковского процесса без последействия. Обнаружено, что введение в систему внутреннего резервирования требует рассмотрения двух альтернативных вариантов модели системы: варианта для случая, в котором объём резервов ограничен возможностями каналов восстановления в системе, и варианта, в котором указанное ограничение отсутствует. Составлены графы состояний системы для указанных режимов функционирования и получены выражения для финальных вероятностей этих состояний. На основе полученных финальных вероятностей составлены аналитические расчётные соотношения для характеристик эффективности системы с замкнутым циклом. В качестве основной характеристики эффективности такого рода систем предлагается использовать вероятность полного функционирования системы, т.е. вероятность её работы с использованием всего объёма активных ресурсов. Представлен числовой пример, подтверждающий работоспособность предложенной модели, и проведён сопоставительный анализ вариантов управления эффективностью замкнутой системы путём изменения объёма резервов, количества процессов восстановления и интенсивности этих процессов. Выявлено доминирующее значение внутренних резервов при обеспечении заданных показателей эффективности системы с замкнутым циклом Here we consider the problem of reproduction of the ability of natural systems to self-repair in artificial objects due to the existence of a closed loop of matter and energy in them. We show that the creation of a closed life cycle in the system presupposes the implementation of the process of restoring resources and their accumulation in the form of internal reserves consumed by the system in unfavorable conditions of existence. We obtained a functional diagram of a closed-loop system and proposed a mathematical model of its functioning in the form of a discrete homogeneous Markov process without aftereffect. We found that the introduction of internal redundancy into the system requires consideration of two alternative options for the system model: the option for the case in which the volume of reserves is limited by the capabilities of the recovery channels in the system, and the option in which the specified limitation is absent. We compiled the graphs of the states of the system for the specified modes of operation and obtained expressions for the final probabilities of these states. On the basis of the obtained final probabilities, we got analytical design ratios for the characteristics of the efficiency of a system with a closed loop. As the main characteristic of the efficiency of such systems, we propose to use the probability of the complete functioning of the system, i.e. the probability of its work using the entire volume of active resources. We present a numerical example that confirms the performance of the proposed model, and carried out a comparative analysis of options for managing the efficiency of a closed-loop system by changing the volume of reserves, the number of recovery processes and the intensity of these processes. We revealed the dominant value of internal reserves while ensuring the specified performance indicators of a closed-loop system

A Markov chain-based model for structural vulnerability assessmentof corrosion-damaged reinforced concrete bridges

The deterioration and cracking of reinforced concrete (RC) bridges due to the chloride-induced corrosion of steel reinforcement is an inherently time-dependent stochastic phenomenon. In the current practice of bridge management systems, however, the determination of the condition states of deteriorated bridges is highly dependent on the opinion of experienced inspectors. Taking such complexity into account, the current paper presents a new stochastic predictive methodology using a non-homogeneous Markov process, which directly relates the visual inspection data (corrosion rate and crack widths) to the structural vulnerability of deteriorated concrete bridges. This methodology predicts the future condition of corrosion-induced damage (concrete cracking) by linking structural vulnerability analysis and a discrete-time Markov chain model. The application of the proposed methodology is demonstrated through a case-study corrosion-damaged RC bridge pier. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

Method of modelling operation and maintenance processes in public transport systems using a certain class of stochastic processes

The study presents a method for application of the theory Markov homogenous processes for modeling of the process of vehicle operational state changes characterized by exponential distribution of their duration time. A model of operation and maintenance of vehicles used in the research object has been developed. The research object is a city bus transport system situated in the analyzed agglomeration. Stochastic process {X(t), t = 0} is a mathematical model of the process of operation and maintenance of public transport buses. The analyzed stochastic process {X(t),t = 0} has a finite phase space S, S={S1, S2, ..., Sn}. It was assumed that operation of the model is to be described by the homogeneous Markov process {X(t) : t ? R+} with a finite set of S states. The states of the analyzed stochastic process correspond to the operational states distinguished for a bus. A hypothetical computing model was built in order to illustrate the discussion and present a method for application of the developed model. The parameters of the model were estimated based on the analysis of initial results of experimental tests conducted in a real bus transport system.

Time-Homogeneous Markov Process for Low Birth Weight Progression under Treatment

Background: Low birth weight incidence is quite high in the sub region, which has a public health concern. The weight of a baby at birth has dire consequences on the child as an infant, in childhood and as an adult. Methods: The aim of this study was to explore and examine the spread and gravity of incidence of low birth weight by using a multi-state model to understand low birth weight progression. This study utilised data by Ghana Statistical Service from Multiple Indicators Cluster Survey conducted in 2011 to monitor progress of children and women. Results: The multi-state Markov model dealt into the low birth weight transitions and severity under three treatments where transition intensities, transition probabilities and the mean sojourn times were estimated which show that low birth weight children tend to spend less time in bad states than in good states. Conclusion: Generally, the survival of a low birth weight child in future time decreases from state 1 to state 4, hence treatment must be applied on time.

A hierarchical approach to model decision making: a study in chemotactic behavior ofEscherichia coli

Reducing the complex behavior of living entities to its underlying physical and chemical processes is a formidable task in biology. Complex behaviors can be characterized as decision making: the ability to process the incoming information via an intracellular network and act upon this information to choose appropriate strategies. Motility is one such behavior that has been the focus many modeling efforts in the past. Our aim is to reduce the chemotactic behavior in E. coli to its molecular constituents in order to paint a comprehensive and end-to-end picture of this intricate behavior. We utilize a hierarchical approach, consisting of three layers, to achieve this goal: at the first level, chemical reactions involved in chemotaxis are simulated. In the second level, the chemical reactions give rise to the mechanical movement of six independent flagella. At the last layer, the two lower layers are combined to allow a digital bacterium to receive information from its environment and swim through it with verve. Our results are in concert with the experimental studies concerning the motility of E. coli cells. In addition, we show that our detailed model of chemotaxis is reducible to a non-homogeneous Markov process.