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作者：Karatzas, I; Sudderth, WD
作者单位：Columbia University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider a process X(.) = {X(t), 0 less than or equal to t < infinity} which takes values in the interval I = (0, 1), satisfies a stochastic differential equation dX(t) = beta(t) dt + sigma(t) dW(t), X(0) = x is an element of I and, when it reaches an endpoint of the interval I, it is absorbed there. Suppose that the parameters beta and sigma are selected by a controller at each instant t is an element of [0, infinity) from a set depending on the current position. Assume also that the controll...
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作者：Norris, JR
作者单位：University of Cambridge
摘要：Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of nonuniqueness is constructed. The stochastic coalescent is shown to converge weakly to the solution of Smoluchowski's equation.
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作者：Wyner, AJ
作者单位：University of Pennsylvania
摘要：Let X = {X-n : n = 1,2,...} be a discrete valued stationary ergodic process distributed according to probability P. Let Z(1)(n) = {Z(1), Z(2),..., Z(n)} be an independent realization of an n-block drawn Kith the same probability as X. We consider the waiting time W-n defined as the first time the n-block Z(1)(n) appears in X. There are many recent results concerning this waiting time that demonstrate asymptotic properties of this random variable. In this paper, we prove that for all n the rand...
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作者：Li, D; Rogers, TD
作者单位：Lakehead University; University of Alberta
摘要：Let D subset of or equal to (-infinity, infinity) be a dosed domain and set xi = inf{x; x is an element of D}. Let the sequence X-(n) = {X-j((n)); j greater than or equal to 1}, n greater than or equal to 1 be associated with the sequence of measurable iterated functions f (n)(x(1), x(2), ..., x(kn)): D-kn -> D (k(n) greater than or equal to 2), n greater than or equal to 1 and some initial sequence X-(0) = {X-j((0)); j greater than or equal to 1} of stationary and m-dependent random variables...
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作者：Borovkova, S; Burton, R; Dehling, H
作者单位：Oregon State University; University of Groningen
摘要：Motivated by the problem of estimating the fractal dimension of a strange attractor, we prove weak consistency of U-statistics for stationary ergodic and mixing sequences when the kernel function is unbounded, extending by this earlier results of Aaronson, Burton, Dehling, Gilat, Hill and Weiss. We apply the obtained results to show consistency of the Takens estimator for the con-elation dimension.
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作者：Iglói, E; Terdik, G
作者单位：University of Debrecen
摘要：The partial derivatives with respect to time and the fractional Brownian motion of a particular class of stationary processes are defined. Although the fractional Brownian motion is not semimartingale, the bilinear SDE with fractional Brownian motion input is considered and solved. The solution is explicitly given in both the frequency and time domains in the case when the coefficient of the bilinear term is pure imaginary. The stationary Stratonovich solution of the bilinear SDE with white no...
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作者：Jagers, P
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：A (general) branching process, where individuals need not reproduce independently, satisfies a homogeneous growth condition if, vaguely, one would not expect the progeny from any one individual to make out more than its proper fraction of the whole population at any time in the future. This notion is made precise, and it is shown how it entails classical Malthusian growth in supercritical cases, in particular for population size-dependent Bienayme-Galton-Watson and Markov branching processes, ...
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作者：Spivak, G; Cvitanic, J
作者单位：Columbia University
摘要：In the framework of continuous-time, Ito processes models for financial markets, we study the problem of maximizing the probability of an agent's wealth at time T being no less than the value C of a contingent claim with expiration time T. The solution to the problem has been known in the context of complete markets and recently also for incomplete markets; we rederive the complete markets solution using a powerful and simple duality method, developed in utility maximization literature. We the...
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作者：Del Moral, P; Guionnet, A
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Several random particle systems approaches were recently suggested to solve nonlinear filtering problems numerically. The present analysis is concerned with genetic-type interacting particle systems. Our aim is to study the fluctuations on path space of such particle-approximating models.
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作者：Cao, J; Worsley, K
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; McGill University
摘要：We introduce two new types of random field. The cross correlation field R(s, t) is the usual sample correlation coefficient for a set of pairs of Gaussian random fields, one sampled at point s is an element of R-M, the other sampled at point t is an element of R-M. The homologous correlation field is defined as R(t) = R(t, t), that is, the diagonal of the cross correlation field restricted to the same location s = t. Although the correlation coefficient can be transformed pointwise to a t-stat...
