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951.
The papers of R. Ramer and S. Kusuoka investigate conditions under which the probability measure induced by a nonlinear transformation on abstract Wiener space(,H,B) is absolutely continuous with respect to the abstract Wiener measure. These conditions reveal the importance of the underlying Hilbert spaceH but involve the spaceB in an essential way. The present paper gives conditions solely based onH and takes as its starting point, a nonlinear transformationT=I+F onH. New sufficient conditions for absolute continuity are given which do not seem easily comparable with those of Kusuoka or Ramer but are more general than those of Buckdahn and Enchev. The Ramer-Itô integral occurring in the expression for the Radon-Nikodym derivative is studied in some detail and, in the general context of white noise theory it is shown to be an anticipative stochastic integral which, under a stronger condition on the weak Gateaux derivative of F is directly related to the Ogawa integral.Research supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92 J 0154 and the Army Research Office Grant No. DAAL 03 92 G 0008. 相似文献
952.
I. A. Taimanov 《Acta Appl Math》1994,36(1-2):119-124
The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier 相似文献
953.
Summary Consider estimating the mean vector from dataN
n
(,
2
I) withl
q
norm loss,q1, when is known to lie in ann-dimensionall
p
ball,p(0, ). For largen, the ratio of minimaxlinear risk to minimax risk can bearbitrarily large ifp
. Obvious exceptions aside, the limiting ratio equals 1 only ifp=q=2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax problem. Whenp, simple non-linear co-ordinatewise threshold rules are asymptotically minimax at small signal-to-noise ratios, and within a bounded factor of asymptotic minimaxity in general. We also give asymptotic evaluations of the minimax linear risk. Our results are basic to a theory of estimation in Besov spaces using wavelet bases (to appear elsewhere). 相似文献
954.
Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos
n
consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos
n
. In particular, we show:
| The diameter of Pos n is 5 for alln>2 (and hence Pos n is connected for alln); | |
| With probability 1, the distance between two members of Pos n is 2; | |
| The graphs Pos n are universal (i.e. every graph occurs as an induced subgraph of some Pos n ); | |
|
The maximal size (n) of an independent set of Pos
n
satisfies the asymptotic formula
|
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