We consider the dynamic pricing problem of perishable products in a system with a constant production rate. Potential demands arrive according to a compound Poisson process, and are price-sensitive. We carry out the sample path analysis of the inventory process and by using level-crossing method, we derive its stationary distribution given a pricing function. Based on the distribution, we express the average profit function. By a stochastic comparison approach, we characterize the pricing strategy given different customers willingness-to-pay functions. Finally, we provide an approximation algorithm to calculate the optimal pricing function.

This paper considers the occurrence of patterns in sequences of independent trials from a finite alphabet; Gani and Irle (1999) have described a finite state automaton which identifies exactly those sequences of symbols containing the specific pattern, which may be thought of as the word of interest. Each word generates a particular Markov chain. Motivated by a result of Guibas and Odlyzko (1981) on stochastic monotonicity for the random times when a particular word is completed for the first time, a new level-crossing ordering is introduced for stochastic processes. A process {Yn : n = 0, 1, …} is slower in level-crossing than a process {Zn}, if it takes {Yn} stochastically longer than {Zn} to exceed any given level. This relation is shown to be useful for the comparison of stochastic automata, and is used to investigate this ordering for Markov chains in discrete time.

We formulate stochastic indicator parameters that characterize pollution levels in geographical regions with heterogeneous contaminant distributions. The indicator parameters are expressed in terms of the random fields representing the contaminant distributions and the critical threshold level specified by health and environmental standards. Certain theoretical results are proven regarding univariate and bivariate indicator parameters. The analytical expressions obtained are general and can be used in practice for various types of contaminant distributions. A test of ergodicity-breaking is suggested for scientific and engineering applications in terms of the indicator parameters. Fractal characteristics of the indicator parameters are discussed. The effects of modelling and observation scale on exceedance contamination analysis are examined. Indicator random field parameters are studied on both continuum and lattice domains using analytical means and numerical simulations.