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61.
Ferenc Weisz 《Transactions of the American Mathematical Society》1996,348(6):2169-2181
We introduce p-quasi-local operators and the two-dimensional
dyadic Hardy spaces defined by the dyadic squares. It is proved that, if a sublinear operator is p-quasi-local and bounded from to , then it is also bounded from to . As an application it is shown that the maximal operator of the Cesàro means of a martingale is bounded from to and is of weak type (1,1) provided that the supremum in the maximal operator is taken over a positive cone. So we obtain the dyadic analogue of a summability result with respect to two-dimensional trigonometric Fourier series due to Marcinkievicz and Zygmund; more exactly, the Cesàro means of a function converge a.e. to the function in question, provided again that the limit is taken over a positive cone. Finally, it is verified that if we take the supremum in a cone, but for two-powers, only, then the maximal operator of the Cesàro means is bounded from to for every .
dyadic Hardy spaces defined by the dyadic squares. It is proved that, if a sublinear operator is p-quasi-local and bounded from to , then it is also bounded from to . As an application it is shown that the maximal operator of the Cesàro means of a martingale is bounded from to and is of weak type (1,1) provided that the supremum in the maximal operator is taken over a positive cone. So we obtain the dyadic analogue of a summability result with respect to two-dimensional trigonometric Fourier series due to Marcinkievicz and Zygmund; more exactly, the Cesàro means of a function converge a.e. to the function in question, provided again that the limit is taken over a positive cone. Finally, it is verified that if we take the supremum in a cone, but for two-powers, only, then the maximal operator of the Cesàro means is bounded from to for every .
62.
63.
We consider filtrations for which all ℋ2 martingales are of integrable variation. We find a sufficient condition and a necessary condition for this property. Both
these conditions are stated in terms the volume of a filtration. The volume of a filtration is defined using a metric on a
space of σ-algebras. To obtain the aforementioned conditions we use two equivalent metrics introduced by Boylan and Rogge. We also prove
that the original definitions of these metrics can be simplified.
相似文献
64.
65.
Alexander Iksanov Konrad Kolesko Matthias Meiners 《Stochastic Processes and their Applications》2019,129(11):4480-4499
Let be Biggins’ martingale associated with a supercritical branching random walk, and let be its almost sure limit. Under a natural condition for the offspring point process in the branching random walk, we show that if the law of belongs to the domain of normal attraction of an -stable distribution for some , then, as , there is weak convergence of the tail process , properly normalized, to a random scale multiple of a stationary autoregressive process of order one with -stable marginals. 相似文献
66.
In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type
of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter
for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function
for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented
to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter.
Accepted 23 July 1999 相似文献
67.
In this paper, we consider the optimal dynamic asset allocation of pension fund with mortality risk and salary risk. The managers of the pension fund try to find the optimal investment policy (optimal asset allocation) to maximize the expected utility of terminal wealth. The market is a combination of financial market and insurance market. The financial market consists of three assets: cashes with stochastic interest rate, stocks and rolling bonds, while the insurance market consists of mortality risk and salary risk. These two non-hedging risks cause incompleteness of the market. By martingale method and dynamic programming principle we first derive the approximate optimal investment policy to overcome the difficulty, then investigate the efficiency of the approximation. Finally, we solve an optimal assets liabilities management(ALM) problem with mortality risk and salary risk under CRRA utility, and reveal the influence of these two risks on the optimal investment policy by numerical illustration. 相似文献
68.
69.
M.L. Kleptsyna A. Le Breton 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):229-251
A Cameron-Martin type formula is derived for the Laplace transform of some integrals of the square of a general continuous Gaussian process. The formula involves in particular the variance of the filtering error in some auxiliary optimal filtering problem which is used in the proof. This variance is expressed in terms of the solution of a Riccati-Volterra type integral equation containing the covariance function of the process. In various specific cases this equation is solved and then the formula becomes completely explicit. 相似文献
70.
Toshio Honda 《Annals of the Institute of Statistical Mathematics》2009,61(2):413-439
We consider nonparametric estimation of marginal density functions of linear processes by using kernel density estimators.
We assume that the innovation processes are i.i.d. and have infinite-variance. We present the asymptotic distributions of
the kernel density estimators with the order of bandwidths fixed as h = cn
−1/5, where n is the sample size. The asymptotic distributions depend on both the coefficients of linear processes and the tail behavior
of the innovations. In some cases, the kernel estimators have the same asymptotic distributions as for i.i.d. observations.
In other cases, the normalized kernel density estimators converge in distribution to stable distributions. A simulation study
is also carried out to examine small sample properties. 相似文献