scholarly journals Realisation of a class of Markov processes through unitary evolutions in Fock space

1991 ◽  
pp. 31-36
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Markov Processes ◽  
Fock Space

On Some Markov Processes Arising from the Eyre-Hudson Super Lie Algebra Representations

1998 ◽  
Vol 01 (03) ◽  
pp. 485-498
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Brownian Motion ◽  
Markov Processes ◽  
Fock Space ◽  
Linear Manifold ◽  
Free Field ◽  
Natural Manner ◽  
Commutation Relations ◽  
Boson Fock Space ◽  
Lie Algebra Representations ◽  
Super Lie Algebra

It is well-known3,5 that Brownian motion and Poisson process arise naturally from the canonical commutation relations (CCR) of free field operators in a boson Fock space. Eyre and Hudson2 have recently shown how to construct fields of operators in a boson Fock space obeying super Lie commutation relations. We establish the essential self-adjointness of their real and imaginary parts on the domain ∊, the linear manifold generated by all the exponential (coherent) vectors and determine a family of Markov processes which they give rise to in a natural manner. These Markov processes yield examples of Evans–Hudson flows3,5 and Azéma-like martingales.1,4,6

Bilinear Markov Processes of Searching for Moving Targets

2001 ◽  
Vol 33 (5-8) ◽  
pp. 13
Author(s):  
Karen G. Dzyubenko ◽  
Arkadiy A. Chikriy
Keyword(s):  
Markov Processes ◽  
Moving Targets

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.

Optimal Control of Markov Processes.

1983 ◽  
Author(s):  
Wendell H. Fleming
Keyword(s):  
Optimal Control ◽  
Markov Processes
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