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Statistical models and analysis of cumulated damage processes
Volf, Petr
The contribution deals with a stochastic process which cumulates random increments at random moments. We derive its martingale - compensator decomposition and then we propose the estimator of characteristics of distribution of increments. An application deals with the process of growing damage of a technical device leading to a break of device when cumulated damage exceeds a certain level. We also discuss the problem of prediction of the cumulative process behaviour.
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Mean variance models in Markovian decision processes: Optimality conditions
Sladký, Karel ; Sitař, M.
We consider a discrete-time Markov reward processes with finite state and action spaces. In contrast with the classical models we assume that the (weighted) long run mean variance, i.e. the (weighted) difference of the ratio of long run second to first moments of total expected reward and the long run average return, is minimized. Ideas for finding optimal long-run average return of Markov and semi-Markov decision processes by policy iterations are heavily employed.
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On economic model of cycles
Vošvrda, Miloslav
The van der Pol's equation with an appropriate feedback is applied to forming of a model of economic cycles. The model exhibits the ability of the savings and investments to give output in a limit cycle by a bifurcation. According to the life cycle hypothesis, the households will have constant, or will continuously increase, the marginal propensity to saving. The savings deviation is accelerated in relation with the gap between the GDP and its potential value.
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