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作者：ALGOET, P
作者单位：Stanford University
摘要：We discuss universal schemes for portfolio selection. When such a scheme is used for investment in a stationary ergodic market with unknown distribution, the compounded capital will grow with the same limiting rate as could be achieved if the infinite past and hence of the distribution of the market were known to begin with. By specializing the market to a Kelly horse race, we obtain a universal scheme for gambling on a stationary ergodic process with values in a finite set. We point out the c...
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作者：EINMAHL, JHJ
摘要：The tail empirical process is defined to be for each n is-an-element-of N, w(n)(t) = (n/k(n))1/2-alpha(n)(tk(n)/n), 0 less-than-or-equal-to t less-than-or-equal-to 1, where alpha(n) is the empirical process based on the first n of a sequence of independent uniform (0, 1) random variables and {k(n)}n=1infinity is a sequence of positive numbers with k(n)/n --> 0 and k(n) --> infinity. In this paper a complete description of the almost sure behavior of the weighted empirical process alpha(n)alpha...
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作者：PITTEL, B
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作者：ROCKNER, M
摘要：We study the positive parabolic functions of the Ornstein-Uhlenbeck operator on an abstract Wiener space E using the approach developed by Dynkin. This involves first proving a characterization of the entrance space of the corresponding Ornstein-Uhlenbeck semigroup and deriving an integral representation for an arbitrary entrance law in terms of extreme ones. It is shown that the Cameron-Martin densities are extreme parabolic functions, but that if dim E = infinity, not every positive paraboli...
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作者：NOBLE, C
作者单位：University System of Ohio; Oberlin College
摘要：The sexual reproduction process is a reaction-diffusion type interacting particle system which exhibits phase transition. In this paper an upper bound is given for the critical value of the reaction rate and the equilibrium density is determined for all noncritical values of the reaction rate. The method of renormalized bond construction is the basis of our proof. Results for the hydrodynamic limit of the process are employed and some results for the associated nonlinear partial differential e...
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作者：SHIEH, NR
摘要：We show that certain d-dimensional Markov processes X(t), t greater-than-or-equal-to 0, have the property that if E is a closed subset of R+ with sufficiently large Hausdorff dimension, then X(E) has k-multiple points. This is applied directly to diffusions driven by stochastic differential equations and Levy processes with positive lower indices, solving problems posed by J. P. Kahane and S. J. Taylor.
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作者：BISHOP, CJ
作者单位：University of California System; University of California Los Angeles
摘要：A planar domain whose boundary E hes in the real line is called a Denjoy domain. In this article we consider some geometric properties of Brownian motion in such a domain. The first result is that if E has zero length (Absolute value of E = 0), then there is a set F subset-of E of full harmonic measure such that every Brownian path which exits at x is-an-element-of F hits both (- infinity, x) and (x, infinity) with probability 1, verifying a conjecture of Burdzy. Next we show that if dim(E) < ...
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作者：LIAO, M
摘要：We prove that if G is a subgroup of the (time-change) symmetry group of a Markov process X(t) which is transitive and has a compact isotropy subgroup, then after a time change, X(t) becomes G-invariant. The symmetry groups of diffusion processes are discussed in more detail. We show that if the generator of X(t) is the Laplacian with respect to the intrinsic metric, then X(t) has the best invariance property.
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作者：SZCZOTKA, W
摘要：Consider a single-server queue with units served in order of arrival for which we can define a stationary distribution (equilibrium distribution) of the vector of the waiting time and the queue size. Denote this vector by (w(rho), l(rho)), where rho < 1 is the traffic intensity in the system when it is in equilibrium and lambda(rho) is the intensity of the arrival stream to this system. Szczotka has shown under some conditions that (1 - rho)(l(rho) - lambda(rho)w(rho)) --> p 0 as p up 1 (in he...
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作者：ATHREYA, KB
摘要：Let {Z(n)} be a p type positively regular nonsingular critical branching process with mean matrix M. If v is a right eigenvector of M for the eigenvalue 1 and Y(n) = Z(n) . v, and if M(n) = max0 less-than-or-equal-to j less-than-or-equal-to n Y(j), then it is shown that under second moments (log n)-1E(i)M(n) --> i . v, where E(i) denotes starting with Z0 = i and . denotes inner product. This is an extension of the result for the single type case obtained by Athreya in 1988.
