Regenerative sets and subordinators

1977 ◽  
Vol 14 (1) ◽  
pp. 217-220
Author(s):  
Cristina Gzyl
Keyword(s):  
Markov Processes ◽  
Probabilistic Structure ◽  
Regenerative Sets

It has been shown that the probabilistic structure of a regular regenerative set can be described in terms of the exponent of an appropriate subordinator. We give a relation which expresses the distribution of two Markov processes associated with a regenerative set in terms of this exponent.

Regenerative sets and subordinators

1977 ◽  
Vol 14 (01) ◽  
pp. 217-220
Author(s):  
Cristina Gzyl
Keyword(s):  
Markov Processes ◽  
Probabilistic Structure ◽  
Regenerative Sets

It has been shown that the probabilistic structure of a regular regenerative set can be described in terms of the exponent of an appropriate subordinator. We give a relation which expresses the distribution of two Markov processes associated with a regenerative set in terms of this exponent.

Hidden Markov Processes

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Hidden Markov Models ◽  
Markov Processes ◽  
Viterbi Algorithm ◽  
Markov Models ◽  
Hidden Markov ◽  
Local Alignment ◽  
Biological Applications ◽  
Standard Material ◽  
Hidden Markov Processes ◽  
Genomics And Proteomics

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. It starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and proteomics. The topics examined include standard material such as the Perron–Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum–Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. It also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored.

Sign in / Sign up

Export Citation Format

Share Document