Displaying similar documents to “Relative entropy and waiting times for continuous-time Markov processes.”

Average convergence rate of the first return time

Geon Choe, Dong Kim (2000)

Colloquium Mathematicae

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The convergence rate of the expectation of the logarithm of the first return time R n , after being properly normalized, is investigated for ergodic Markov chains. I. Kontoyiannis showed that for any β > 0 we have l o g [ R n ( x ) P n ( x ) ] = o ( n β ) a.s. for aperiodic cases and A. J. Wyner proved that for any ε >0 we have - ( 1 + ε ) l o g n ≤ l o g [ R n ( x ) P n ( x ) ] ≤ l o g l o g n eventually, a.s., where P n ( x ) is the probability of the initial n-block in x. In this paper we prove that E [ l o g R ( L , S ) - ( L - 1 ) h ] converges to a constant depending only on the process where R ( L , S ) is the modified first return...

Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

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We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around 5 . 10 4 instead of 10 8 .

A constant in pluripotential theory

Zbigniew Błocki (1992)

Annales Polonici Mathematici

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We compute the constant sup ( 1 / d e g P ) ( m a x S l o g | P | - ∫ S l o g | P | d σ ) : P a polynomial in ℂ n , where S denotes the euclidean unit sphere in ℂ n and σ its unitary surface measure.