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1.
Abstract

The method of random integral representation, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note, we show that a composition of two random integral mappings β is again a random integral mapping. We illustrate our results with some examples.  相似文献   

2.
The existence of sparse pseudorandom distributions is proved. These are probability distributions concentrated in a very small set of strings, yet it is infeasible for any polynomial-time algorithm to distinguish between truly random coins and coins selected according to these distributions. It is shown that such distributions can be generated by (nonpolynomial) probabilistic algorithms, while probabilistic polynomial-time algorithms cannot even approximate all the pseudorandom distributions. Moreover, we show the existence of evasive pseudorandom distributions which are not only sparse, but also have the property that no polynomial-time algorithm may find an element in their support, except for a negligible probability. All these results are proved independently of any intractability assumption.  相似文献   

3.
The compound negative binomial model,introduced in this paper,is a discrete time version.We discuss the Markov properties of the surplus process,and study the ruin probability and the joint distributions of actuarial random vectors in this model.By the strong Markov property and the mass function of a defective renewal sequence,we obtain the explicit expressions of the ruin probability,the finite-horizon ruin probability,the joint distributions of T,U(T-1),|U(T)| and 0≤inn相似文献   

4.
We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples. Received: October 1998 / Accepted: June 2000?Published online October 18, 2000  相似文献   

5.
An inductive procedure is used to obtain distributions and probability densities for the sum Sn of independent, non-equally uniform random variables. Some known results are then shown to follow immediately as special cases. Under the assumption of equally uniform random variables some new formulas are obtained for probabilities and means related to Sn. Finally, some new recursive formulas involving distributions are derived.  相似文献   

6.
We develop a general method for the construction of a probability structure on the space F of random sets in ℝ. For this purpose, by using the introduced notion of c-system, we prove a theorem on the unique extension of a finite measure from a c-system to the minimal c-algebra. The obtained structure of measurability enables one to determine probability distributions of the c-algebra of random events sufficient, e.g., for the so-called fractal dimensionality of random realizations to be considered as a measurable functional on F.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1467–1483, November, 2004.  相似文献   

7.
Summary The inclusion functional of a random convex set, evaluated at a fixed convex set K, measures the probability that the random convex set contains K. This functional is an analogue of the complement of the distribution function of an ordinary random variable. A methodology is described for evaluating the inclusion functional for the case where the random convex set is generated as the convex hull of n i.i.d. points from a distribution function F in the plane. For general K and F, the inclusion probability is difficult to compute in closed form. The case where K is a straight line segment is examined in detail and, in this situation, a simple answer is given for an interesting class of distributions F.  相似文献   

8.
Monte Carlo algorithms typically need to generate random variates from a probability distribution described by an unnormalized density or probability mass function. Perfect simulation algorithms generate random variates exactly from these distributions, but have a running time T that is itself an unbounded random variable. This article shows that commonly used protocols for creating perfect simulation algorithms, such as Coupling From the Past can be used in such a fashion that the running time is unlikely to be very much larger than the expected running time. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008  相似文献   

9.
Summary For a bounded linear operator Q, on a Banach space E, and a real number , there are introduced classes, U (Q), of some limit distributions such that U O(I coincides with the Lévy class L 0. Elements from U (Q are characterized in terms of convolution equations and as probability distributions of some random integral functionals. The continuity and fixed points of this random mapping is studied. It is shown that fixed points coincide with the class of Q-stable measures.This work partially supported by AFOSR Grant No. F49620 82 C 0009  相似文献   

10.
Letψ andϕ be two given random closed sets in a locally compact second countable topological spaceS. (They need not be based on the same probability space.) The main result gives necessary and sufficient conditions on the distributions ofψ andϕ, for the existence of two random closed sets and , based on the same probability space and such that their distributions coincide with those ofψ andϕ, resp., and a.s. This coupling result tells us in particular when a probability distribution onS is selectionable w.r.t. (the distribution of) a random closed set. An existence result for realizable thinnings of a simple point process is obtained by specializing it to supports of random measures. The coupling result is extended to random variables in a countably based continuous poset. As examples we mention various kinds of random capacities — in particular random measures — and random compact (saturated) sets. Moreover, the extended result tells us when a probability distribution onS is selectionable w.r.t. the distribution of a random compact (saturated) set.  相似文献   

11.
Summary Some criteria based on K-L information number andW-divergence are presented for a certain type of uniform approximate equivalence of two probability distributions. As applications, some necessary and sufficient conditions are also given for the corresponding uniform asymptotic equivalence of two random sequences. The Institute of Statistical Mathematics  相似文献   

12.
13.
We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time–space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environment (DPRE), for which the quantity called the free energy is well studied. We discuss the survival probability (both global and local) for BRWRE and give a criterion for its positivity in terms of the free energy of the associated DPRE. We also show that the global growth rate for the number of particles in BRWRE is given by the free energy of the associated DPRE, though the local growth rate is given by the directional free energy.  相似文献   

14.
The sample-based rule obtained from Bayes classification rule by replacing the unknown parameters by ML estimates from a stratified training sample is used for the classification of a random observationX into one ofL populations. The asymptotic expansions in terms of the inverses of the training sample sizes for cross-validation, apparent and plug-in error rates are found. These are used to compare estimation methods of the error rate for a wide range of regular distributions as probability models for considered populations. The optimal training sample allocation minimizing the asymptotic expected error regret is found in the cases of widely applicable, positively skewed distributions (Rayleigh and Maxwell distributions). These probability models for populations are often met in ecology and biology. The results indicate that equal training sample sizes for each populations sometimes are not optimal, even when prior probabilities of populations are equal.  相似文献   

15.
《Optimization》2012,61(1):123-135
Let m denote the infimum of the Integral of a function q w r t all probability measures with given marginals. The determination of m is of interest for a series of stochastic problems. In the present paper we prove a duality theorem for the determination of m and give some examples for its application. We consider especially the problem of extremal variance of sums of random variables and prove a theorem for the existence of random variables with given marginal distributions, such that their sum has variance zero.  相似文献   

16.
《Quaestiones Mathematicae》2013,36(4):307-344
Sattolo's algorithm creates a random cyclic permutation by interchanging pairs of elements in an appropriate manner; the Fisher-Yates algorithm produces random (not necessarily cyclic) permutations in a very similar way. The distributions of the movements of the elements in these two algorithms have already been treated quite extensively in past works. In this paper, we are interested in the joint distribution of two elements j and k; we are able to compute the bivariate generating functions explicitly, although it is quite involved. From it, moments and limiting distributions can be deduced. Furthermore, we compute the probability that elements i and j ever change places in both algorithms.  相似文献   

17.
This paper presents a systematic study of the class of multivariate distributions obtained by a Gaussian randomization of jumps of a Lévy process. This class, called the class of type G distributions, constitutes a closed convolution semigroup of the family of symmetric infinitely divisible probability measures. Spectral form of Lévy measures of type G distributions is obtained and it is shown that type G property can not be determined by one dimensional projections. Conditionally Gaussian structure of type G random vectors is exhibited via series representations.  相似文献   

18.
We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of p-moments, p>0, as well as exponential moments. In particular, a formula for the abscissa of convergence of the moment generating function is provided. The results are illustrated with a number of examples at the end of the article.   相似文献   

19.
We prove that the probability of each second order monadic property of a random mapping un converges as n→∞. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 277–295, 1997  相似文献   

20.
We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such as degree sequence, shape, and total length are derived. An interpretation is given in terms of sampling from the inhomogeneous continuum random tree of Aldous and Pitman (1998). ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 176–195, 1999  相似文献   

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