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作者：Hsu, EP
作者单位：Northwestern University
摘要：We discuss angular convergence of Riemannian Brownian motion on a Cartan-Hadamard manifold and show that the Dirichlet problem at infinity for such a manifold is uniquely solvable under the curvature conditions -Ce(2-eta)ar(x) less than or equal to K-M(x) less than or equal to -a(2) (eta > 0) and -Cr(x)(2beta) less than or equal to K-M(x) less than or equal to -alpha(alpha - 1)/r(x)(2) (alpha > beta + 2 > 2), respectively.
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作者：Soner, HM; Touzi, N
作者单位：Koc University; Institut Polytechnique de Paris; ENSAE Paris
摘要：A smooth solution {Gamma(t)}(tis an element of[0,T]) subset of R-d of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem. In this control problem the controller tries to steer the state process into a given deterministic set T with probability one. The reachability set, V(t), for the target problem is the set of all initial data x from which the state process X-X(v)(t) is an element of T for some control process v. This representation is proved b...
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作者：Stannat, W
作者单位：University of Bielefeld
摘要：We study the global properties of transition semigroups (p(t)(nu,Psi,A)) of (A, Psi)-superprocesses over compact type spaces with possibly nonzero immigration nu in various function spaces. In particular, we compare the different rates of convergence of (p(t)(nu,Psi,A)) to equilibrium. Our analysis is based on an explicit formula for the Gateaux derivative of p(t)(nu,Psi,A) F.
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作者：Crisan, D
作者单位：Imperial College London
摘要：In Crisan, Gaines and Lyons [SIAM J Appl. Probab. 58 (1998) 313-3421 we describe a branching particle algorithm that produces a particle approximation to the solution of the Zakai equation and find an upper bound for the rate of convergence of the mean square error. In this paper, the exact rate of convergence of the mean square error is deduced. Also, several variations of the branching algorithm with better rates of convergence are introduced.
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作者：Gyöngy, I; Krylov, N
作者单位：University of Edinburgh; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider two stochastic partial differential equations du(epsilon)(t) = (L(r)u(epsilon)(t) + f(r)(t))dV(epsilont)(r) + (M(k)u(epsilon)(t) + g(k)(t)) odY(t)(k), epsilon = 0, 1, driven by the same multidimensional martingale Y = (Y-k) and by different increasing processes V-0(r), V-1(r), r = 1, 2,..., d(1), where L-r and M-k are second- and first-order partial differential operators and o stands for the Stratonovich differential. We estimate the moments of the supremum in t of the Sobolev nor...
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作者：Hwang, HK
作者单位：Academia Sinica - Taiwan
摘要：We study the convergence rate to normal limit law for the space requirement of random m-ary search trees. While it is known that the random variable is asymptotically normally distributed for 3 less than or equal to m less than or equal to 26 and that the limit law does not exist for m > 26, we show that the convergence rate is O(n(-1/2)) for 3 less than or equal to m less than or equal to 19 and is O(n(-3(3/2-alpha))), where 4/3 < alpha < 3/2 is a parameter depending on m for 20 less than or ...
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作者：Seppäläinen, T; Sethuraman, S
作者单位：University of Wisconsin System; University of Wisconsin Madison; Iowa State University
摘要：Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at density rho. Place a second-class particle initially at the origin. For the case rho not equal 1/2 we show that the time spent by the second-class particle at the origin has finite expectation. This strong transience is then used to prove that variances of additive functionals of local mean-zero functi...
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作者：Gao, F; Hannig, J; Torcaso, F
作者单位：University of Idaho; Colorado State University System; Colorado State University Fort Collins; Johns Hopkins University
摘要：We will introduce a class of m-times integrated Brownian motions. The exact asymptotic expansions for the L-2-small ball probabilities will be discussed for members of this class, of which the usual m-times integrated Brownian motion is an example. Another example will be what we call an Euler-integrated Brownian motion. We will also find very sharp estimates for the asymptotics of the eigenvalues of the covariance operator of integrated Brownian motions and will, therefore, obtain exact, not ...
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作者：Shirai, T; Takahashi, Y
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology; Kanazawa University; Kyoto University
摘要：We construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants. Under a mild condition they turn out unique Gibbs measures. Also some ergodic properties, including the entropy positivity, are discussed in the lattice case.
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作者：Guillin, A
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Consider the following stochastic differential equation in R-d: dX(t)(epsilon) = b(X-t(epsilon), xi(t/epsilon)) dt + rootepsilona(X-t(epsilon), xi(t/epsilon)) dW(t), X-0(epsilon) = X-0, where the random environment (xi(t)) is an exponentially ergodic Markov process, independent of the Wiener process (W-t), with invariant probability measure pi, and epsilon is some small parameter. In this paper we prove the moderate deviations for the averaging principle of X-epsilon, that is, deviations of (X...
