This thesis investigates the effect of time interval omission on properties and distributions of stochastic processes obtained by aggregating the state space of the original process into a finite number of subsets. Time interval omission is a phenomenon of missing sojourns of the aggregated process that are shorter than a certain duration, which results in an apparent, rather than the ideal, sequence of sojourns. This problem arises in the stochastic modelling of ion channels, where the underlying Markov process is not observable and only the apparent aggregated process can be reconstructed from experimental data. The methodology employed in the thesis includes embedding a Markovian sequence that contains all information about the apparent aggregated process <I>Z (t), </I>into the original process. Distributions of <I>Z (t)</I> are deduced from characteristics of an intermediary semi-Markov apparent gateway process <I>Y (t)</I>, determined by this sequence. We also construct several fundamental matrix functions of time such that probability distributions of <I>Y (t)</I> can be expressed via these functions and a unified efficient algorithm for their calculation exists for all values 0 < <I>t</I> < ∞. Three particular problems are analysed in greater detail. The multi-level model of time interval omission leads to a new enhanced definition of apparent sojourns and to the introduction of the concept of indeterminacy. Investigation of the piece-wise homogeneous model of the underlying process provides new practical tools for the analysis of pulse and single jump experiments. Explicit probability distributions are obtained for the developed time interval omission model of structural bursts. Along with the theoretical results for probability distributions of <I>Z (t)</I>, software is developed as a part of the research that provides a flexible tool for calculating various characteristics of <I>Y (t)</I> and <I>Z (t)</I>. Numerical examples considered in the thesis show the applicability of the developed methods and demonstrate non-trivial effects of time interval omission.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:638180 |
| Date | January 1995 |
| Creators | Merlushkin, A. I. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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