Asymptotic analysis of risk quantities conditional on ruin for multidimensional heavy-tailed random walks

In this paper we consider a multidimensional renewal risk model with regularly varying claims. This model may be used to describe the surplus of an insurance company possessing several lines of business where a large claim possibly puts multiple lines in a risky condition. Conditional on the occurrence of ruin, we develop asymptotic approximations for the average accumulated number of claims leading the process to a rare set, and the expected total amount of shortfalls to this set in finite and infinite horizons. Furthermore, for the continuous time case, asymptotic results regarding the total occupation time of the process in a rare set and time-integrated amount of shortfalls to a rare set are obtained.     

Dynamics of Branched Continuous-Discrete Systems Towed in Rough Water

A method is proposed for dynamic analysis of towed spatial branched structures. The method permits determining the kinematic and force characteristics of a structure towed either downwave or upwave. The slacking of certain elements of the structure and changed speed of its motion are taken into account. The dynamics of a specific system is analyzed in the cases of abruptly changing towing speed and towing in regularly rough water with different wave parameters __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 84–89, October 2005.     

一种场站设置问题中的几个结论

本文研究如下一种场站设置问题:设S是欧空间E~m中由有限个点A_1,A_2,…,A_n组成的集合.d(A_i,A_j)表示点A_i和A_j之间的距离.令σ(S)=Σ_(1≤i相似文献   

CRISPR-Cas System for RNA Detection and Imaging

The system of clustered regularly interspaced short palindromic repeats(CRISPR)and CRISPR-associated endonucleases(Cas)have been widely used in gene editing,disease treatment,molecular diagnosis and chromosome imaging.On account of the programmable target recognition of CRISPR-Cas system and the specific targeting function toward RNA of type Ⅵ class Ⅱ Cas proteins,CRISPR-Cas system has been deployed as RNA recognition and detection tools,exhibiting promising application potentials in the field of RNA detection and imaging.In this review,we summarize the latest research progresses as well as development prospects of CRISPR-Cas system in RNA diagnosis and live cell RNA imaging.     

The relation between non-bossiness and monotonicity

It is a well-known fact that in some economic environments, non-bossiness and monotonicity are interrelated. In this paper, we have presented a new domain-richness condition called weak monotonic closedness, on which non-bossiness in conjunction with individual monotonicity is equivalent to monotonicity. Moreover, by applying our main result to several types of economies, we have obtained characterizations in terms of non-bossiness.     

Refined discrete regular variation and its applications

We introduce a new class of the so‐called regularly varying sequences with respect to τ and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to τ. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.     

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??In this paper, we prove the existence and uniqueness of solutions for reflected backward stochastic differential equations driven by a Levy process, in which the reflecting barriers are just right continuous with left limits whose jumps are arbitrary. To derive the above results, the monotonic limit theorem of Backward SDE associated with Levy process is established.     

The time discretization in classes of integro‐differential equations with completely monotonic kernels: Weighted asymptotic convergence

We consider the time discretization for the solution of the equation with . Here, the operators L_j are densely defined positive self‐adjoint linear operator on a Hilbert space H and have spectral decompositions with respect to a common resolution of the identity in H . The kernel functions , are assumed to be completely monotonic on (0,∞) and locally integrable, but not constant. The considered time discretization method comes from [Da Xu, Science China Mathematics 56 (2013), 395–424], where the backward Euler method is combined with order one convolution quadrature for approximating the integral term. In this article, the convergence properties of the time discretization are given in the weighted and norm, where ρ is a given weighted function. Numerical experiments show the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 896–935, 2016     

一类具脉冲效应和单调功能反应的时滞捕食系统的正周期解

利用重合度理论中的延拓定理,获得了一类具有脉冲效应和单调功能反应的时滞捕食系统正周期解存在性的充分条件.最后,通过列举三个例子表示我们等待结果的有效性.     

Computing the Topological Entropy for Piecewise Monotonic Maps on the Interval

A new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented. It uses a transition matrix associated with the transformation. For this matrix we give a spectral theorem. This can be used for an estimation of the accuracy of the algorithm.