Detailed Balance

Detailed Balance

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and statistical mechanics, a Markov process is said to have detailed balance if the transition probability, P, between each pair of states i and j in the state space obey: where P is the Markov transition matrix (transition probability), i.e., Pij = P(Xt = j - Xt 1 = i); and i and j are the equilibrium probabilities of being in states i and j, respectively. When Pr(Xt 1 = i) = i for all i, this is equivalent to the joint probability matrix, Pr(Xt 1 = i, Xt = j) being symmetric in i and j; or symmetric in t 1 and t. The definition carries over straightforwardly to continuous variables, where becomes a probability density, and P(s, s) a transition kernel probability density from state s to state s: A Markov process that has detailed balance is said to be a reversible Markov process or reversible Markov chain.show more

Product details

  • Paperback | 96 pages
  • 152 x 229 x 6mm | 150g
  • Acu Publishing
  • United States
  • English
  • 6136728028
  • 9786136728025