TY - JOUR
T1 - Occupation time distributions for the telegraph process
AU - Bogachev, Leonid
AU - Ratanov, Nikita
N1 - Funding Information:
L. Bogachev was partially supported by a Leverhulme Research Fellowship. Both authors gratefully acknowledge partial support by the London Mathematical Society (through an LMS Scheme 2 Grant) during N. Ratanov’s visit to the University of Leeds in June 2007, when part of this research was done. We are grateful to the anonymous Associate Editor for a query that encouraged us to work out a probabilistic proof of Theorem 2.4 based on the diffusion approximation ( Appendix A.3 ).
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/8
Y1 - 2011/8
N2 - For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.
AB - For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of subnormal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.
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U2 - 10.1016/j.spa.2011.03.016
DO - 10.1016/j.spa.2011.03.016
M3 - Article
AN - SCOPUS:79958100700
SN - 0304-4149
VL - 121
SP - 1816
EP - 1844
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 8
ER -