On random motions with velocities alternating at Erlang-distributed random times (Q2759816)
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scientific article; zbMATH DE number 1683786
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On random motions with velocities alternating at Erlang-distributed random times |
scientific article; zbMATH DE number 1683786 |
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On random motions with velocities alternating at Erlang-distributed random times (English)
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18 December 2001
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telegrapher process
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alternating renewal process
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pseudo-Bessel function
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distribution of the maximum
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0.9052007
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0.8966022
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0.87610805
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0.8693933
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0.86258715
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0.8624177
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0.8613086
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0.86067235
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0.85864294
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The following generalization of the telegrapher's process is considered: a particle on the real line alternates between moving to the right with velocity \(c>0\) and to the left with velocity \(v>0\), such that the instants of direction reversal form an alternating renewal process. The probability distribution of the particle's location and velocity at time \(t\) is studied. When the inter-renewal times are Erlang, this distribution is expressed in terms of pseudo-Bessel functions. Some numerical examples are given. Finally, there is a short discussion of the maximum of the process over a bounded time interval.
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