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作者：Durrett, R
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作者：Fleming, WH; Sheu, SJ
作者单位：Brown University; Academia Sinica - Taiwan
摘要：An optimal investment policy model for the long term growth of expected utility of wealth is considered. The utility function is HARA with exponent -infinity < gamma < 1. The problem can be reformulated as an infinite time horizon, risk sensitive control problem. Then the dynamic programming equations for different HARA exponents and different policy constraints are studied. We obtain some estimates for the solution of each equation. This can be used to derive an optimal policy with some inter...
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作者：Krone, SM
作者单位：University of Idaho
摘要：We introduce a multitype interacting particle system, which is a natural generalization of the contact process. Here, individuals in the population have two life stages, young and adult. Only adults can give birth and each new offspring is young. Transition from young to adult occurs at constant rate, and individuals die at rates that depend on their life stage. Important to the analysis of this process is the construction of a multitype dual process.
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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, ...
