1-inkdot alternating pushdown automaton is a slightly modified alternating pushdown automaton with the additional power of marking at most 1 tape-cell on the input （with an inkdot） once. This paper investigates the ...1-inkdot alternating pushdown automaton is a slightly modified alternating pushdown automaton with the additional power of marking at most 1 tape-cell on the input （with an inkdot） once. This paper investigates the closure property of sublogarithmic space-bounded 1-inkdot alternating pushdown automata with only existential （universal） states, and shows, for example, that for any function L（n） such that L（n） ≥ log logn and L（n） = o（log n）, the class of sets accepted by weakly （strongly） L（n） space-bounded 1-inkdot two-way alternating pushdown automata with only existential （universal） states is not closed under concatenation with regular sets, length-preserving homomorphism, and Kleene closure.展开更多
A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of life...A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.展开更多
We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of t...We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.展开更多
In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumpti...In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumptions of X and Y. Under the assumption that Y has decreasing reverse hazard rate (DAHR), we show that if X is in any one of the classes IFR, DFR, DMRL or IMRL then XY is in the same class as X. We also obtain some useful bounds for the distribution and the moment of XY. Because the idle time in classical GI/G/1 queuing system can be regarded as the residual life at random time, the results obtained in this paper have applications in the study of such system.展开更多
基金This work is supported by the National Natural Science Foundation of China under Grant No. 60403012,
文摘1-inkdot alternating pushdown automaton is a slightly modified alternating pushdown automaton with the additional power of marking at most 1 tape-cell on the input （with an inkdot） once. This paper investigates the closure property of sublogarithmic space-bounded 1-inkdot alternating pushdown automata with only existential （universal） states, and shows, for example, that for any function L（n） such that L（n） ≥ log logn and L（n） = o（log n）, the class of sets accepted by weakly （strongly） L（n） space-bounded 1-inkdot two-way alternating pushdown automata with only existential （universal） states is not closed under concatenation with regular sets, length-preserving homomorphism, and Kleene closure.
基金The National Natural Science Foundation of China(No. 10801032)
文摘A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.
基金Acknowledgements The authors were grateful to the two reviewers for their valuable comments and suggestions to improve the present paper. This work was supported by the National Natural Science Foundation of China （NO. 11071182） and the Doctor Introduction Foundation of Nantong University （No. 12R066）.
文摘We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.
基金the National Natural Science Foundation of China.
文摘In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumptions of X and Y. Under the assumption that Y has decreasing reverse hazard rate (DAHR), we show that if X is in any one of the classes IFR, DFR, DMRL or IMRL then XY is in the same class as X. We also obtain some useful bounds for the distribution and the moment of XY. Because the idle time in classical GI/G/1 queuing system can be regarded as the residual life at random time, the results obtained in this paper have applications in the study of such system.
