Y. V. Prohorov and Y. A. Rozanov, Probability Theory, Springer-Verlag, 1969.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and the conjugate densities of the mixture components. If it is assumed that each mixture component is non degenerate, i.e. k 0, then c k1 ; c k2 ; c kT is a sequence of T i.i.d. random variables with a non degenerate distributionand lim sup T 1 t=1 c kt = 1 with probability one [25]. It follows that w k converges to t=1 c kt =T with probability one when T 1. Applying the same reasoning to m k and r k , it can be seen that the EM reestimation formulas for the MAP and ML approaches are asymptotically similar. Thus as long as the initial estimates of are identical, ....

Y. V. Prohorov and Y. A. Rozanov, Probability Theory, Springer-Verlag, 1969.

....paths on can proceed as follows. Consider a onedimensional process dx(t) x; t)dt oe(x; t)dB(t) Suppose that at time t the particle is at location x(t) x. Now for the location at time t dt take x(t dt) x Sigma oe(x; t) p dt with prob 1 2 Sigma (x; t) 2oe(x; t) p dt See [17, 22]. In the bivariate case one generates x and y processes. Figure 1 presents examples of such simulations in the case of the process dr(t) Gamma rH(r)dt dB(t) and two particular potential functions. In the first example H(r; t) r r, i.e. the process is Ornstein Uhlenbeck reverting to the ....

Prohorov, Yu. V. and Rozanov, Yu. A. (1969). Probability Theory. SpringerVerlag, New York.

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Prohorov, Y. V. & Rozanov, Y. A., Probability Theory (Springer, Berlin, 1969).

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