13,288 research outputs found
Values in Water
Inaugural speech spoken in acceptance of the chair āEthics of water engineeringā at the Faculty of Technology, Policy and Management of Delft University of Technology on 16 November 2018
On associated polynomials and decay rates for birth-death processes
We consider sequences of orthogonal polynomials and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials. In particular, we relate the supports of the two measures, and their moments. As an application we analyse the relation between two decay rates connected with a birth-death process. \u
Associated polynomials and birth-death processes
We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to applications in the setting of birth-death processes. In particular, we relate the supports of the two measures, and their moments of positive and negative orders. Our results indicate how the prevalence of recurrence or -recurrence in a birth-death process can be recognized from certain properties of an associated measure. \u
Connectivity of circulant digraphs
An explicit expression is derived for the connectivity of circulant digraphs
On the Strong Ratio Limit Property for Discrete-Time Birth-Death Processes
A sufficient condition is obtained for a discrete-time birth-death process to
possess the strong ratio limit property, directly in terms of the one-step
transition probabilities of the process. The condition encompasses all
previously known sufficient conditions
Sven Ove Hanssonās contribution to Philosophy of Technology and Engineering
Paper presented at the symposium on the occasion of the retirement of Sven Ove Hansson. The symposium took place on 13-14 December 2019 at the Royal Institute of Technology in Stockholm, Sweden
Asymptotic period of an aperiodic Markov chain
We introduce the concept of asymptotic period for an irreducible and
aperiodic, discrete-time Markov chain X on a countable state space, and develop
the theory leading to its formal definition. The asymptotic period of X equals
one - its period - if X is recurrent, but may be larger than one if X is
transient; X is asymptotically aperiodic if its asymptotic period equals one.
Some sufficient conditions for asymptotic aperiodicity are presented. The
asymptotic period of a birth-death process on the nonnegative integers is
studied in detail and shown to be equal to 1, 2 or infinity. Criteria for the
occurrence of each value in terms of the 1-step transition probabilities are
established.Comment: 19 page
The indeterminate rate problem for birth-death processes
A birth-death process is completely determined by its set of rates if and only if this set satisfies a certain condition C, say. If for a set of rates R the condition C is not fulfilled, then the problem arises of characterizing all birth-death processes which have rate set R (the indeterminate rate problem associated with R). We show that the characterization may be effected by means of the decay parameter, and we determine the set of possible values for the decay parameter in terms of JR. A fundamental role in our analysis is played by a duality concept for rate sets, which, if the pertinent rate sets satisfy C, obviously leads to a duality concept for birth-death processes. The latter can be stated in a form which suggests the possibility of extension in the context of indeterminate rate problems. This, however, is shown to be only partially true
On the Ī±-classification of birth-death and quasi-birth-death processes
In several recent papers criteria for the Ī±-classification of birth-death and quasi-birth-death processes have been proposed. In this paper the relations between the various criteria are brought to light
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