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By Engler D. A.

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Throughout this paper we assume that 0: is a a-finite measure on E such that 1. , IE Pt! do: = IE f do:, "It ;::: 0 and f ;::: OJ 2. the dual Markov semigroup (Pt), acting on LOO(o:), of (Pt} on £1(0:) can be realized as the semigroup of transition kernels (Ft(x,dy)) of a continuous Hunt-Markov process (JP>x)xEE on n = C(lR+,E) (the dual process). , without interaction potential). In the simplest quantum mechanical case of a system of particles in a potential, it will be the Brownian Motion on E = lRd (in the flat case) or a Riemannian manifold.

If (¢', 'IjJ') is another such couple, then there is a constant C > 0 such that ¢=C¢', 'IjJ 1 , = C'IjJ, a-a. e. Proof. Notice that (Pt ) is strictly positive improving (well known, see [35, p. 1). 14) and similarly (q',p') corresponding to (¢', 'IjJ'). 9). 2, it is unique by Proposition 1. e. e. e. 15) in [-00, +00), by Fubini's theorem. , then there would be -00 :'5 a < b < +00, such that a(logq -logq' :'5 a) /\ a(1ogqlog q' ~ b) > o. e. 15). e .. e. for some constant C > O. e. too. 4. 9), especially for the time reversal.

1). 14) and similarly (q',p') corresponding to (¢', 'IjJ'). 9). 2, it is unique by Proposition 1. e. e. e. 15) in [-00, +00), by Fubini's theorem. , then there would be -00 :'5 a < b < +00, such that a(logq -logq' :'5 a) /\ a(1ogqlog q' ~ b) > o. e. 15). e .. e. for some constant C > O. e. too. 4. 9), especially for the time reversal. See §4, 5. 5. 8) is verified. 16b) 4. Lo(dX) > -00. L ® Pi') < +00, as desired. Ll has been given by Beurling (14). See also [7). 3 The Least Action Principle We extend the least action principle for Bernstein processes [1, 8) to the general setting of Section 1.

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A pseudolikelihood approach for simultaneous analysis of array comparative genomic hybridizations (2 by Engler D. A.


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