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991.
Izidor Gertner 《Stochastic Processes and their Applications》1978,7(3):231-246
The structure of a nonlinear filter with observation process having continuous and discontinuous components is considered. The approach is based on the so-called “Bayes” formula for conditional expectations. “Fubini” type theorems for stochastic integrals are given and used to obtain the representations of an optimal estimate and of the conditional likelihood ratio. A linear unnormalized filtering equation for controlled system process is derived. 相似文献
992.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
993.
A purely combinatorial construction of the quantum cohomology ring of the generalized flag manifold is presented. We show that the ring we construct is commutative, associative and satisfies the usual grading condition. By using results of our previous papers [12, 13], we obtain a presentation of this ring in terms of generators and relations, and formulas for quantum Giambelli polynomials. We show that these polynomials satisfy a certain orthogonality property, which—for G = SLn(
)—was proved previously in the paper [5]. 相似文献
994.
Uwe Khler 《中国科学A辑(英文版)》2005,48(2):145-154
Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B, dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solvable in hyperbolic harmonic Bergman spaces. Furthermore we investigate the boundary behavior of the solutions of Gleason type problem. 相似文献
995.
Several improvements are made to an algorithm of Higham and Smith for computing the matrix cosine. The original algorithm
scales the matrix by a power of 2 to bring the ∞-norm to 1 or less, evaluates the [8/8] Padé approximant, then uses the double-angle
formula cos (2A)=2cos 2A−I to recover the cosine of the original matrix. The first improvement is to phrase truncation error bounds in terms of ‖A2‖1/2 instead of the (no smaller and potentially much larger quantity) ‖A‖. The second is to choose the degree of the Padé approximant to minimize the computational cost subject to achieving a desired
truncation error. A third improvement is to use an absolute, rather than relative, error criterion in the choice of Padé approximant;
this allows the use of higher degree approximants without worsening an a priori error bound. Our theory and experiments show
that each of these modifications brings a reduction in computational cost. Moreover, because the modifications tend to reduce
the number of double-angle steps they usually result in a more accurate computed cosine in floating point arithmetic. We also
derive an algorithm for computing both cos (A) and sin (A), by adapting the ideas developed for the cosine and intertwining the cosine and sine double angle recurrences.
AMS subject classification 65F30
Numerical Analysis Report 461, Manchester Centre for Computational Mathematics, February 2005.
Gareth I. Hargreaves: This work was supported by an Engineering and Physical Sciences Research Council Ph.D. Studentship.
Nicholas J. Higham: This work was supported by Engineering and Physical Sciences Research Council grant GR/T08739 and by a
Royal Society–Wolfson Research Merit Award. 相似文献
996.
There are many known asymptotic estimates for the expected number of real zeros of a random algebraic polynomial The coefficients are mostly assumed to be independent identical normal random variables with mean zero and variance unity. In this case, for all sufficiently large, the above expected value is shown to be . Also, it is known that if the have non-identical variance , then the expected number of real zeros increases to . It is, therefore, natural to assume that for other classes of distributions of the coefficients in which the variance of the coefficients is picked at the middle term, we would also expect a greater number of zeros than . In this work for two different choices of variance for the coefficients we show that this is not the case. Although we show asymptotically that there is some increase in the number of real zeros, they still remain . In fact, so far the case of is the only case that can significantly increase the expected number of real zeros.
997.
We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a -finite measure space, Lorentz function spaces on a -finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.
998.
We introduce a generalized notion of the zeta regularization. As applications we show the quantum analogue of the Lerch formula
and of the Dirichlet class number formulas. We also give some further examples related to Appell's O-functions.
2000 Mathematics Subject Classification: Primary—11M36
Work in part supported by Grant-in Aid for Scientific Research (B) No. 11440010, and by Grant-in Aid for Exploratory Research
No. 13874004, Japan Society for the Promotion of Science. 相似文献
999.
This paper develops algebraic and convergence properties of the left and right block reflectors used in the block diagonalization algorithm. Several numerical illustrations are reported.AMS subject classification (2000) 65F20, 15A23.Submitted December 2002. Accepted October 2003. Communicated by Per Christian Hansen. 相似文献
1000.
The ChowlaSelberg formula is applied in approximatinga given Epstein zeta function. Partial sums of the series derivefrom the ChowlaSelberg formula, and although these partialsums satisfy a functional equation, as does an Epstein zetafunction, they do not possess an Euler product. What we callpartial sums throughout this paper may be considered as specialcases concerning a more general function satisfying a functionalequation only. In this article we study the distribution ofzeros of the function. We show that in any strip containingthe critical line, all but finitely many zeros of the functionare simple and on the critical line. For many Epstein zeta functionswe show that all but finitely many non-trivial zeros of partialsums in the ChowlaSelberg formula are simple and on thecritical line. 2000 Mathematics Subject Classification 11M26. 相似文献