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We obtain conditions under which a Stratonovich integral equation driven by a continuous p-semimartingale has a weak solution and a unique strong solution-measure. Generalization of the Wong–Zakai theorem and the convergence rate of the corresponding approximation are given.
Let P be a probability distribution on a locally compact separable metric space (S,d). We study the following problem of approximation of a distribution P by a set A from a given class
We prove upper and lower bounds for fractional moments of zeta-functions attached to certain cusp forms on the critical line; the upper bound being conditional subject to the truth of the Riemann hypothesis.
It is well known that the generalized regression (GREG) estimator of the finite population total is asymptotically unbiased. Consequently, bias is negligible when the sample size is large. But the magnitude of the bias is not known, if we are estimating small areas or operating with small...
In this paper, we continue an asymptotic analysis of a stochastic version of the Lotka–Volterra model for predator–prey interactions. While the fluid approximation and large deviations were shown in Klebaner and Liptser (Ann. Appl. Probab. 11, 1263–1291, 2001) here we establish the diffusion...
The subject of the paper is the probability-theoretic properties of elementary symmetric polynomials σ
of arbitrary degree k in random variables X
(i=1,2,…,m) defined on special subsets of commutative rings ℛ
with identity of finite characteristic m. It is shown that the probability...
Asymptotic distances between probability distributions appearing in πps sampling theory are studied. The distributions are Poisson, Conditional Poisson (CP), Sampford, Pareto, Adjusted CP and Adjusted Pareto sampling. We start with the Kullback-Leibler divergence and the Hellinger distance and...
A joint discrete limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved.
The report deals exclusively with stability of characterizations where unimprovable results have been obtained, i.e., the modulus (measure) of stability is exactly calculated.
We obtain upper and lower bounds for the power moments of additive functions on random permutations. The main ideas of proofs have been originated in probabilistic number theory.
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