Optimal Sequential Estimation for Markov-Additive Processes

1998 ◽  
pp. 167-181 ◽  
Author(s):  
Ryszard Magiera
Keyword(s):  
Sequential Estimation ◽  
Additive Processes ◽  
Markov Additive Processes

scholarly journals First Passage Times for Markov Additive Processes with Positive Jumps of Phase Type

2008 ◽  
Vol 45 (03) ◽  
pp. 779-799 ◽  
Author(s):  
Lothar Breuer
Keyword(s):  
Inverse Function ◽  
First Passage Times ◽  
Phase Type Distribution ◽  
First Passage ◽  
Additive Processes ◽  
Special Cases ◽  
Phase Type ◽  
Spectrally Negative Lévy Processes ◽  
Passage Times ◽  
Markov Additive Processes

The present paper generalises some results for spectrally negative Lévy processes to the setting of Markov additive processes (MAPs). A prominent role is assumed by the first passage times, which will be determined in terms of their Laplace transforms. These have the form of a phase-type distribution, with a rate matrix that can be regarded as an inverse function of the cumulant matrix. A numerically stable iteration to compute this matrix is given. The theory is first developed for MAPs without positive jumps and then extended to include positive jumps having phase-type distributions. Numerical and analytical examples show agreement with existing results in special cases.

scholarly journals A Note on Wiener–Hopf Factorization for Markov Additive Processes

2012 ◽  
Vol 27 (1) ◽  
pp. 202-219 ◽  
Author(s):  
Przemysław Klusik ◽  
Zbigniew Palmowski
Keyword(s):  
Additive Processes ◽  
Markov Additive Processes
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