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991.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献
992.
Let (
t
)
t>0 be a symmetric weakly continuous semigroup of probability measures on a nonabelien complete separable group G and let v be its Lévy measure. The purpose of this paper is to provide a relatively simple proof of the zero-one law for semigroups with the Lévy measure satisfying either v(H
c) = or v(H
c) = 0. 相似文献
993.
Tomoyuki Shirai 《Journal of statistical physics》1998,90(5-6):1449-1459
We consider the expectation of the determinant det(–X)–1for Im >0 associated with some random N×Nmatrices and factorize it into NStieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N. 相似文献
994.
We consider perturbed empirical distribution functions
, where {Ginn, n1} is a sequence of continuous distribution functions converging weakly to the distribution function of unit mass at 0, and {X
i, i1} is a non-stationary sequence of absolutely regular random variables. We derive the almost sure representation and the law of the iterated logarithm for the statistic
whereU
n
is aU-statistic based onX
1,...,X
n
. The results obtained extend or generalize the results of Nadaraya,(7) Winter,(16) Puri and Ralescu,(9,10) Oodaira and Yoshihara,(8) and Yoshihara,(19) among others.Research supported by the Office of Naval Research Contract N00014-91-J-1020. 相似文献
995.
Suppose 0t
1<t
2<... are fixed points in time. At timet
k
, a unit with magnitudeX
k
and lifetimeL
k
enters a population or is placed into a system. Suppose that theX
k
's are i.i.d. withEX
1=, theL
k
's are i.i.d., and that theX
k
's andL
k
's are independent. In this paper we find conditions under which the continuous time process Avr{X
k
:t
k
t<t
k
+L
k
} is almost surely convergent to . We also demonstrate the sharpness of these conditions. 相似文献
996.
LetX
1,X
2,..., be a sequence ofi.i.d. random variables with a moment generating function finite in a neighborhood of 0. Further, for each integern1, letS
n
denote the sum of the firstn terms in this sequence. We study the extended large deviation of such sums, meaning,P{S
n
>n
n
}, where
n
is any sequence converging to infinity. We also derive functional extended large deviation theorems and then apply them to obtain functional versions of the Erdös-Rényi strong law of large numbers.Research partially supported by an NSF Grant. 相似文献
997.
Raoult's law as applied to binary solvent mixtures 总被引:1,自引:0,他引:1
The inapplicability of the original statement of Raoult's law to binary solvent mixtures has been known for many years. An appropriate form for binary solvent mixtures is developed from the fundamental thermodynamic concept of fugacity, and is shown to be quantitatively applicable to the water+tetrahydrofuran solvent system and qualitatively applicable to the results which have been obtained for other aqueous organic solvent mixtures. 相似文献
998.
Petra Küster 《Stochastic Processes and their Applications》1984,17(2):313-325
Let {Zt} be an increasing Markov process on N n and {σ(k)} the corresponding sequence of jump times. Let the increments of Zt be i.i.d. with finite expectation and covariances, and let where h and ? are sufficiently smooth positive functions and ?Zt? = ∑nj=1Zt(j), Zt=(Zt(1),…,Zt(n)). While a linear f results in asymptotically exponential growth, a suitable class of sublinear f leads to a growth asymptotically at most that of a power. Covering both cases, we obtain analoga of the strong LLN, the CLT and LIL. 相似文献
999.
Let , 0<aT?T<∞, and {W(t);0?t<∞} be a standard Wiener process. This exposition studies the almost sure behaviour of , under varying conditions on aT and T/aT. The following analogue of Lévy's modulus of continuity of a Wiener Process is also given: and this may be viewed as the exact “modulus of non-differentiability” of a Wiener Process. 相似文献
1000.
Polystyrene supported Rh(I) AA′ (AA′ = anthranilic acid, 2,2′-bipyridine or 1,10-phenanthroline) complexes catalyse the hydrogenation
of monoolefins (terminal, cyclic and internal) and dienes. Ethyl sorbate undergoes saturation via the monoene intermediate.
Thiscis olefin reacts faster than thetrans isomer. The rate law for the reaction is: Rate α [catalyst] [substrate] [H2]. 相似文献