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作者：Burton, Robert M.; Faris, William G.
作者单位：Oregon State University; University of Arizona
摘要：The state of the self-organizing cluster process is a finite subset of points in a bounded region. This subset represents an evolving discrete approximation to a continuous probability distribution in the region. The dynamics of the process is determined by an independent sequence of random points in the region chosen according to the distribution. At each time step the random point attracts the nearest point in the finite set. In this way the subset learns to approximate its environment. It i...
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作者：Kwiecinski, Andrzej; Szekli, Ryszard
作者单位：University of Hamburg; University of Wroclaw
摘要：Point processes on the positive real axis which are positively self-exciting in a sense expressed by their martingale dynamics are studied in this paper. It is shown that such processes can be realized as increasing mappings of Poisson processes and are therefore associated in appropriate manners. Some examples are presented, including Hawkes, renewal, Polya-Lundberg, Markov dependent, semi-Markov, in addition to other point processes. As corollaries an extension of theBurton-Waymire associati...
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作者：Feigin, Paul D.; Kratz, Marie F.; Resnick, Sidney I.
作者单位：Technion Israel Institute of Technology; Cornell University
摘要：This paper continues the study of time series models generated by nonnegative innovations which was begun by Feigin and Resnick. We concentrate on moving average processes. Estimators for moving average coefficients are proposed and consistency and asymptotic distributions established for the case of an order-one moving average assuming either the right or the left tail of the innovation distribution is regularly varying. The rate of convergence can be superior to that of the Yule-Walker or ma...
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作者：Duffie, Darrell; Schroder, Mark; Skiadas, Costis
作者单位：Stanford University; State University of New York (SUNY) System; University at Buffalo, SUNY; Northwestern University
摘要：We derive the implications of default risk for valuation of securities in an abstract setting in which the fractional default recovery rate and the hazard rate for default may depend on the market value of the instrument itself, or on the market values of other instruments issued by the same entity (which are determined simultaneously). A key technique is the use of backward recursive stochastic integral equations. We characterize the dependence of the market value on the manner of resolution ...
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作者：Barbour, A. D.; Heesterbeek, J. A. P.; Luchsinger, C. J.
作者单位：University of Zurich
摘要：We investigate the initial behavior of a deterministic model of parasitic infection, appropriate to transmission between homogeneously mixing hosts, where the amount of infection which is transferred from one host to another at a single contact depends on the number of parasites in the infecting host. In this model, R-0 can be defined to be the lifetime expected number of offspring of an adult parasite under ideal conditions, but it does not necessarily contain the information needed to separa...
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作者：Lent, Janice; Mahmoud, Hosam M.
作者单位：George Washington University
摘要：Using the concept of a tree-growing'' search strategy, we prove that for most practical insertion sorting algorithms, the number of comparisons needed to sort n keys has asymptotically normal behavior. We prove and apply a sufficient condition for asymptotically normal behavior. The condition specifies a relationship between the variance of the number of comparisons and the rate of growth in height of the sequence of trees that the search strategy grows.''
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作者：Davis, Richard A.; Resnick, Sidney I.
作者单位：Colorado State University System; Colorado State University Fort Collins; Cornell University
摘要：We consider a simple stationary bilinear model X-t = cX(t-1) Z(t-1) + Z(t,) t = 0, +/- 1, +/- 2,..., generated by heavy- tailed noise variables {Z(t)}. A complete analysis of weak limit behavior is given by means of a point process analysis. A striking feature of this analysis is that the sample correlation converges in distribution to a nondegenerate limit. A warning is sounded about trying to detect nonlinearities in heavy-tailed models by means of the sample correlation function.
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作者：Perman, Mihael; Wellner, Jon A.
作者单位：University of Ljubljana; University of Washington; University of Washington Seattle
摘要：We study the distributions of the areas under the positive parts of a Brownian motion process B and a Brownian bridge process U: with A(+) = integral B-1(0)+ (t) dt and A(0)(+) = integral U-1(0)+ (t) dt, we use excursion theory to show that the Laplace transforms psi(1) (s) = E exp(-sA(1)) and psi(1)(0) (s) = E exp(-sA(0)(+)) of A(+) and A(0)(+) satisfy integral(infinity)(0)e(-lambda s)psi(+)(root 2s(3/2)) ds = lambda(-1/2)Ai(lambda) + (1/3-integral(lambda)(0)Ai(t)dt)/root lambda Ai(lambda)-Ai...
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作者：Ethier, S. N.
作者单位：Utah System of Higher Education; University of Utah
摘要：Oscar's system is a gambling system in which the aim is to win one betting unit, at least with high probability, and then start over again. The system can be modeled by an irreducible Markov chain in a subset of the two-dimensional integer lattice. We show that the Markov chain, which depends on a parameter p representing the single-trial win probability, is transient if p < 1/2 and positive recurrent if p >= 1/2
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作者：Fill, James Allen; Mahmoud, Hosam M.; Szpankowski, Wojciech
作者单位：Johns Hopkins University; George Washington University; Purdue University System; Purdue University
摘要：We investigate the duration of an elimination process for identifying a winner by coin tossing or, equivalently, the height of a random incomplete trie. Applications of the process include the election of a leader in a computer network. Using direct probabilistic arguments we obtain exact expressions for the discrete distribution and the moments of the height. Elementary approximation techniques then yield asymptotics for the distribution. We show that no limiting distribution exists, as the a...
