An asymptotic relationship for ruin probabilities under heavy-tailed claims

The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy \(R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)\) if the claim sizes are heavy-tailed, where F_e denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.     

Atmospheric,hydrological and oceanic comprehensive contributions to seasonal polar wobble of Earth Rotation

The geophysical quantitative excitation on seasonal polar wobble of Earth Rotation has not been well achieved so far. The atmospheric, hydrologic and oceanic angular momentum variations are investigated from monthly values simulated by a coupled ocean-atmosphere general circulation model. The simulated equatorial AAM functions agree well with that from the JMA operational analysis in 90°:E direction, but disagree along Greenwich meridian. As for the annual cycle, not only the hydrologic and oceanic excitations partly match the residuals between geodetic functions of polar wobble and JMA AAM functions, but also the combinations with NCEP and JMA analysis AAM functions are better than those estimated from NCAR-CSM1 climate model.     

The structure of blocks

In this paper, we focus on the structure of p-blocks with defect group satisfying some special condition. These special conditions include: two elements of the defect group are conjugate to each other in defect D if and only if they are conjugate to each other in G; the number of conjugacy classes whose p-part is contained in P by conjugacy is not larger than ∣P∣     

Strong conjugation actions induced by flags of exact Borel subalgebras

Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u^-1eCeu.     

Weighted inequalities for real-analytic functions in ℝ<Superscript>2</Superscript>

Let ƒ and g be real-analytic functions near the origin in ℝ². Given 1 < p < ∞, we obtain a characterization of the set of positive numbers ∈ and δ that ensures

Dubrovin Valuation Skew Group Rings

Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given. Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised. Received June 8, 1999, Revised June 4, 2001, Accepted July 20, 2001     

Computing determinantal representation of generalized inverses

We investigate implementation of the determinantal representation of generalized inverses for complex and rational matrices in the symbolic package MATHEMATICA. We also introduce an implementation which is applicable to sparse matrices.     

On convergence of wavelet packet expansions

It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.     

New Wavelet Bases and Isometric Between Symbolic Operators Spaces $$ {\text{OP}}S^{m}_{{1,\delta }} $$ and Kernel Distributions Spaces

In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distribution spaces     

Factorization Index for Completely Positive Graphs

In this paper, we prove that the set of all factorization indices of a completely positive graph has no gaps. In other words, we give an affirmative answer to a question raised by N. Kogan and A. Berman [8] in the case of completely positive graphs. Received December 9, 1997, Accepted May 16, 2002