Occupation times and beyond
نویسندگان
چکیده
منابع مشابه
Occupation times and Bessel densities
Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous time random walk on Z and represent the one state occup...
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This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (see [13]) in the field of Single Molecule FRET spectroscopy. There, a single molecule fluctuates between two or more states, and the experimental observable depends on the state’s occupation time distribution. To mathematically describe the observable there was a need to calcula...
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We determine the distributions of occupation times of a Markov-modulated Brownian motion (MMBM) in separate intervals before a first passage time or an exit from an interval. They will be derived in terms of their Laplace transforms, distinguishing occupation times in different phases too. For MMBMs with strictly positive variation parameters we further propose scale functions.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2002
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(01)00125-9