Large deviation principles for telegraph processes
The aim of this paper is to present large deviation results for some telegraph random motions. We are not aware of any other results of this kind except the ones for the classical telegraph process (with drift). We start with the large deviation principle of the conditional laws given the number of changes of direction for the classical case; moreover, we compare the rate function with the one obtained for the non-conditional distributions. Finally, we study an inhomogeneous model and a planar telegraph motion.
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Volume (Year): 82 (2012)
Issue (Month): 11 ()
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References listed on IDEAS
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- Foong, S. K. & Kanno, S., 1994. "Properties of the telegrapher's random process with or without a trap," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 147-173, September.
- Iacus, Stefano Maria, 2001.
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Elsevier, vol. 55(1), pages 83-88, November.
- Stefano Iacus, 2001. "Statistical analysis of the inhomogeneous telegrapher's process," Departmental Working Papers 2001-02, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
- Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 575-583.
- Macci, Claudio, 2009. "Convergence of large deviation rates based on a link between wave governed random motions and ruin processes," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 255-263, January.
- Orsingher, Enzo, 1990. "Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 49-66, February.
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