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1.
We give a necessary and sufficient condition on a sequence of functions on a set Ω under which there is a measure on Ω which
renders the given sequence of functions a martingale. Further such a measure is unique if we impose a natural maximum entropy
condition on the conditional probabilities. 相似文献
2.
Rasul A. Khan 《Journal of Theoretical Probability》2009,22(2):348-364
The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also
given for martingales (supermartingales) under suitable conditions.
相似文献
3.
A. Račkauskas 《Lithuanian Mathematical Journal》1997,37(4):402-415
Let (ξ
k
,F
k
) be a martingale difference sequence. The paper concerns the tail behavior of the quadratic formS
n
= ∑
k=1
n
∑
j=1
k−1
β
n
k−j
χ
k
χ
j
, where β
n
asn→∞. The main conclusions aboutP}n
−1
S
n
>x
n
}, wherex
n
→∞, asn→∞, are obtained using the tail behavior of a martingale with values in a certain Hilbert space.
Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published
in Lietuvos Matematikos Rinkinys, Vol. 37, No. 4, pp. 532–549, October–December, 1997. 相似文献
4.
A. Dubickas 《Lithuanian Mathematical Journal》1995,35(4):328-332
We give a lower bound for |α−1|, where α is an algebraic number, and also an upper bound for the number of real zeros of a
polynomial. A lower bound for the maximal modulus of conjugates of a totally real algebraic integer is also obtained.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp.
421–431, October–December, 1995. 相似文献
5.
In this article, we introduce a conditional marginal model for longitudinal data, in which the residuals form a martingale
difference sequence. This model allows us to consider a rich class of estimating equations which contains several estimating
equations proposed in the literature. A particular sequence of estimating equations in this class contains a random matrix
R
i−1*(β) as a replacement for the “true” conditional correlation matrix of the ith individual. Using the approach of [12], we identify some sufficient conditions under which this particular sequence of
equations is asymptotically optimal (in our class). In the second part of the article, we identify a second set of conditions
under which we prove the existence and strong consistency of a sequence of estimators of β defined as roots of estimation equations which are martingale transforms (in particular, roots of the sequence of asymptotically
optimal equations). 相似文献
6.
Wen Chi KUO Coenraad C. A. LABUSCHAGNE Bruce A. WATSON 《数学学报(英文版)》2008,24(2):329-342
The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math.,15(2004), 435-451). Here we extend the definition of an asymptotic martingale (amart) to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced. 相似文献
7.
François Coquet Ying Hu Jean Mémin Shige Peng 《Probability Theory and Related Fields》2002,123(1):1-27
From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive,
under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingale. We prove that
any such nonlinear martingale can be represented as the solution of a backward stochastic equation, and in particular admits
continuous paths. In other words, it is a g-martingale.
Received: 2 February 2000 / Revised version: 1 June 2001 / Published online: 13 May 2002 相似文献
8.
A. Laurinčikas 《Lithuanian Mathematical Journal》1999,39(1):51-57
The joint limit distribution of functions given by Dirichlet series is studied. The necessary and sufficient condition when
this distribution is a product of marginal distributions is found. An example of such Dirichlet series with linear independent
systems of exponents is presented.
Partially supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2006 Vilnius; Šiauliai University, P. Višinskio 25, 5419 Šiauliai, Lithuania. Translated
from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 65–73, January–March, 1999.
Translated by A. Laurinčikas 相似文献
9.
A. Baddeley J. Møller A. G. Pakes 《Annals of the Institute of Statistical Mathematics》2008,60(3):627-649
For any point process in that has a Papangelou conditional intensity λ, we define a random measure of ‘innovations’ which has mean zero. When the
point process model parameters are estimated from data, there is an analogous random measure of ‘residuals’. We analyse properties
of the innovations and residuals, including first and second moments, conditional independence, a martingale property, and
lack of correlation. Some large sample asymptotics are studied. We derive the marginal distribution of smoothed residuals
by solving a distributional equivalence. 相似文献
10.
V. Mackevičius 《Lithuanian Mathematical Journal》1992,32(2):227-237
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp.
285–298, April–June, 1992. 相似文献
11.
A. Laurinčikas 《Lithuanian Mathematical Journal》1999,39(3):262-272
Using some conjectures on the mean-value of generalized numbers, limit theorems in the sense of the weak convergence of probability
measures for the Dirichlet series related to the Euler function are proved. Also, the limit measure is studied.
Partially supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania: Šiauliai University, P. Višinskio 25, 5400 Šiauliai, Lithuania.
Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 331–342, July–September, 1999.
Translated by A. Laurinčikas 相似文献
12.
K. V. Navickis 《Lithuanian Mathematical Journal》1999,39(2):203-215
We consider intrinsic normalizations of a hyperplane distribution on the Grassmann manifold of ann-dimensional projective space.
Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2,
pp. 257–273, April–June, 1999.
Translated by V. Mackevičius 相似文献
13.
P. P. Katauskis 《Lithuanian Mathematical Journal》1992,32(2):188-197
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2,
pp. 237–248, April–June, 1992. 相似文献
14.
A. Domarkas 《Lithuanian Mathematical Journal》1995,35(2):144-150
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2,
pp. 181–189, April–June, 1995. 相似文献
15.
È. G. Kir'yatskii 《Lithuanian Mathematical Journal》1995,35(4):373-387
Vilnius Technical University, Saulétekio al. 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys Vol.
35, No. 4, pp. 469–488, October–December, 1995. 相似文献
16.
The asymptotical behavior of the distributions of stochastic processes defined by multiplicative functions in the set of shifted
primes is considered.
The first author was supported by Konferenz der deutschen Akademien der Wissenschaften.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Paderborn University, Warburger 100, 33098 Paderborn, Germany.
Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 441–460, October–December, 1999. 相似文献
17.
Large deviations in a centered Poisson approximation are examined. For lattice distributions, the centered Poisson approximation
is more universal than the normal and standard Poisson laws.
Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1,
pp. 9–23, January–March, 1999.
Translated by V. Čekanavičius 相似文献
18.
A. Dubickas 《Lithuanian Mathematical Journal》1997,37(1):13-19
Let α be an algebraic integer of degreed whosed conjugates are all real. We give a lower bound for the absolute value of conjugates of α in terms ofd and of the number of conjugates outside the interval [−2; 2]. Combining this with a lower bound for Mahler's measure of a
polynomial, we obtain a lower bound for the maximal conjugate of a totally real algebraic integer.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 1, pp.
18–25, January–March, 1997. 相似文献
19.
A. Dubickas 《Lithuanian Mathematical Journal》1999,39(2):168-172
Suppose that ɛ is a positive number, and letd be a sufficiently large positive integer. We consider a set of monic polynomials of degreed with integer coefficients and roots lying in the disk of radiusd
ɛ/d. We prove that the number of such polynomials is less than exp(d
2/3+ɛ).
Partially supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp.
214–219, April–June, 1999. 相似文献
20.
L. Maliaukiené 《Lithuanian Mathematical Journal》1995,35(4):411-417
Vilnius Pedagogical University, Studentų 39, 2034 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35,
No. 4, pp. 518–526, October–December, 1995. 相似文献