scholarly journals Transformation of Markov processes by multiplicative functionals

1965 ◽  
Vol 15 (1) ◽  
pp. 13-30 ◽  
Author(s):  
K. Ito ◽  
S. Watanabe
Keyword(s):  
Markov Processes ◽  
Multiplicative Functionals

On the optimal search for a target whose motion is a Markov process

1973 ◽  
Vol 10 (4) ◽  
pp. 847-856 ◽  
Author(s):  
Lauri Saretsalo
Keyword(s):  
Markov Process ◽  
Euclidean Space ◽  
Markov Processes ◽  
General Condition ◽  
Necessary Condition ◽  
Dimensional Euclidean Space ◽  
Optimal Search ◽  
Continuous Transition ◽  
Transition Functions ◽  
Multiplicative Functionals

We will consider the optimal search for a target whose motion is a Markov process. The classical detection law leads to the use of multiplicative functionals and the search is equivalent to the termination of the Markov process with a termination density. A general condition for the optimality is derived and for Markov processes in n-dimensional Euclidean space with continuous transition functions we derive a simple necessary condition which generalizes the result of Hellman (1972).

On the optimal search for a target whose motion is a Markov process

1973 ◽  
Vol 10 (04) ◽  
pp. 847-856 ◽  
Author(s):  
Lauri Saretsalo
Keyword(s):  
Markov Process ◽  
Euclidean Space ◽  
Markov Processes ◽  
General Condition ◽  
Necessary Condition ◽  
Dimensional Euclidean Space ◽  
Optimal Search ◽  
Continuous Transition ◽  
Transition Functions ◽  
Multiplicative Functionals

We will consider the optimal search for a target whose motion is a Markov process. The classical detection law leads to the use of multiplicative functionals and the search is equivalent to the termination of the Markov process with a termination density. A general condition for the optimality is derived and for Markov processes in n-dimensional Euclidean space with continuous transition functions we derive a simple necessary condition which generalizes the result of Hellman (1972).

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.

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