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作者：BENJAMINI, I; PERES, Y
作者单位：Yale University
摘要：We study a variant of branching Markov chains in which the branching is governed by a fixed deterministic tree T rather than a Galton-Watson process. Sample path properties of these chains are determined by an interplay of the tree structure and the transition probabilities. For instance, there exists an infinite path in T with a bounded trajectory iff the Hausdorff dimension of T is greater than log(1/rho) where rho is the spectral radius of the transition matrix.
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作者：KOURITZIN, MA; HEUNIS, AJ
作者单位：University of Waterloo
摘要：Consider the following random ordinary differential equation: X(epsilon)(tau) = F(X(epsilon)(tau), (tau/epsilon, omega) subject to X(epsilon)(0) = x0, where {F(x, t, omega), t > 0} are stochastic processes indexed by x in R(d), and the dependence on x is sufficiently regular to ensure that the equation has a unique solution X(epsilon)(tau, omega) over the interval 0 less-than-or-equal-to T less-than-or-equal-to 1 for each epsilon > 0. Under rather general conditions one can associate with the ...
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作者：SLUD, EV
摘要：Let X = (X(t),t greater than or equal to 0) be a stationary Gaussian process with zero mean, continuous spectral distribution and twice-differentiable correlation function. An explicit representation is given for the number N-psi(T) of crossings of a C-1 curve psi by X on the bounded interval [0, T], in a multiple Wiener-It (o) over cap integral expansion. This continues work of the author in which the result was given for psi equivalent to 0. The representation is applied to prove new central...
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作者：WU, YD
摘要：In this paper we consider a multilevel branching diffusion particle system and its diffusion approximation, which can be characterized as an M(M(R(d)))-valued process. The long term behavior of the limiting process is studied. The main results are that if d less-than-or-equal-to 4, then the two level M(M(R(d)))-valued process suffers local extinction, and if d = 4, then the process has a self-similarity property.
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作者：CHAMAYOU, JF; LETAC, G
摘要：Let X1 be a (d x d) random stochastic matrix such that the rows of X1 are independent, with Dirichlet distributions. The rows of the (d x d) matrix A are the parameters of these Dirichlet distributions, and we assume that the sums of the rows and columns of A provide the same vector r = (r1,...,r(d)). If (X(n))(n=1)infinity are i.i.d., we prove that lim(n-->infinity)(X(n)...X1) almost surely has identical rows, which are Dirichlet distributed with parameter r. Van Assche has proved this for d ...
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作者：SCHWEIZER, M
摘要：Let X be a semimartingale and Theta the space of all predictable X-integrable processes theta such that integral theta dX is in the space S-2 of semimartingales, we consider the problem of approximating a given random variable H epsilon L(2) by a stochastic integral integral(0)(T) theta(s) dX(s), with respect to the L(2)-norm. If X is special and has the form X = X(0) +M+ integral alpha d(M), we construct a solution in feedback form under the assumptions that integral alpha(2)d(M) is determini...
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作者：BASS, RF; BURDZY, K; KHOSHNEVISAN, D
作者单位：Utah System of Higher Education; University of Utah
摘要：For each a is-an-element-of (0, 1/2), there exists a random measure beta(alpha) which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure beta(alpha) is carried by a set which has Hausdorff dimension equal to 2 - alpha. A Palm measure interpretation of beta(alpha) is given.
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作者：WU, LM
摘要：Let (X(n))n greater-than-or-equal-to 1 be a sequence of i.i.d. r.v.'s with values in a measurable space (E, E) of law mu, and consider the empirical process L(n)(f) = (1/n)SIGMA(k=1)n f(X(k)) with f varying in a class of bounded functions F. Using a recent isoperimetric inequality of Talagrand, we obtain the necessary and sufficient conditions for the large deviation estimations, the moderate deviation estimations and the LIL of L(n)(.) in the Banach space of bounded functionals l(infinity)(F)...
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作者：BOLTHAUSEN, E; DENHOLLANDER, F
作者单位：Utrecht University
摘要：Let W(t) be the Wiener sausage in R(d), that is, the a-neighborhood for some a > 0 of the path of Brownian motion up to time t. It is shown that integrals of the type integral0(t)nu(s)d\W(s)\, with t --> nu(t) nonincreasing and nu(t) approximately nut(-gamma), t --> infinity, have a large deviation behavior similar to that of \W(t)\established by Donsker and Varadhan. Such a result gives information about the survival asymptotics for Brownian motion in a Poisson field of spherical traps of rad...
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作者：ISCOE, I; MCDONALD, D
作者单位：University of Ottawa
摘要：General conditions on general state space Markov jump processes are established for the asymptotic exponentiality of the distribution of the exit time into any small forbidden set. The error bounds for this exponential approximation tend to 0 as the size of the forbidden set tends to 0.
