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作者：KENDALL, WS
摘要：An upper bound is given for the behaviour of the radial part of a Gamma-martingale, generalizing previous work of the author on the radial part of Riemannian Brownian motion. This upper bound is applied to establish an integral curvature condition to determine when Gamma-martingales cannot ''implode'' in finite intrinsic time, answering a question of Emery and generalizing work of Hsu on the C-0-diffusion property of Brownian motion.
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作者：RIO, E
摘要：This paper contains some extension of Kolmogorov's maximal inequality to dependent sequences. Next we derive dependent Marcinkiewicz-Zygmund type strong laws of large numbers from this inequality. In particular, for stationary strongly mixing sequences (X(i))(i) (is an element of) (Z) with sequence of mixing coefficients (alpha(n))(n greater than or equal to 0), the Marcinkiewicz-Zygmund SLLN of order p holds if integral(0)(1)[alpha(-1)(t)](p-1)Q(p)(t) dt < infinity, where alpha(-1) denotes th...
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作者：Pinsky, RG
摘要：Consider the supercritical super-Brownian motion X(t, .) on R(d) corresponding to the evolution equation u(t) = D/2 Delta u + u - u(2). We obtain rather tight bounds on P-mu(X(s, B-n(c)(0)) = 0, for all s is an element of [0, t]) and on P-mu(X(t, B-n(c)(0)) = 0), for large n, where P-mu denotes the measure corresponding to the supercritical super-Brownian motion starting from the finite measure, mu, B-n(0) subset of R(d) denotes the ball of radius n centered at the origin and B-n(c)(0) denotes...
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作者：Stong, R
摘要：In this paper we discuss and apply a novel method for bounding the eigenvalues of a random walk on a group G (or equivalently on its Cayley graph). This method works by looking at the action of an Abelian normal subgroup H of G on G. We may then choose eigenvectors which fall into representations of H. One is then left with a large number (one for each representation of H) of easier problems to analyze. This analysis is carried out by new geometric methods. This method allows us to give bounds...
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作者：HOUDRE, C
摘要：Let (X(n)) be, for example, a weakly stationary sequence or a lacunary system with finite pth moment, 1 less than or equal to p less than or equal to 2, and let {a(n)} be a sequence of scalars. We obtain here conditions which ensure the almost sure convergence of the series Sigma a(n)X(n). When {X(n)} is an orthonormal sequence, the classical Rademacher-Menchov theorem is recovered. This is then applied to study the strong consistency of least squares estimates in multiple regression models.
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作者：LEURIDAN, C
摘要：Let B be a brownian motion starting at 0. We denote by L(t)(*) = max x is an element of R L(t)(*) the maximum of local times at time t. The Barlow-Yor inequalities tell us that for every p > 0, there are constants C-p > c(p) > 0 such that for every stopping time tau, c(p)E[tau(p/2)]less than or equal to E[L(tau)*(p)]less than or equal to C(p)E[tau(p/2)]. Given a fixed closed set F subset of R, we give a condition on F which is necessary and sufficient to derive similar inequalities with max(x ...
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作者：ALEXANDER, KS
摘要：The structure of a spanning forest that generalizes the minimal spanning tree is considered for infinite graphs with a value f(b) attached to each bond b. Of particular interest are stationary random graphs; examples include a lattice with lid uniform values f(b) and the Voronoi or complete graph on the sites of a Poisson process, with f(b) the length of b. The corresponding percolation models are Bernoulli bond percolation and the ''lily pad'' model of continuum percolation, respectively. It ...
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作者：BOLTHAUSEN, E; DEUSCHEL, JD; TAMURA, Y
作者单位：Technical University of Berlin; Keio University
摘要：We are investigating Markov process expectations for large time of the form exp(TF(L(T))), where L(T) is the empirical measure of a uniformly ergodic Markov process and F is a smooth functional. Such expressions are evaluated up to a factor which converges to 1. In contrast to earlier work on the subject, it is not assumed that the process is reversible.
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作者：PESZAT, S; ZABCZYK, J
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：It is shown that the transition semigroup (P-t)(t greater than or equal to 0) corresponding to a nonlinear stochastic evolution equation is strong Feller and irreducible, provided the nonlinearities are Lipschitz continuous and the diffusion term is nondegenerate. This result ensures the uniqueness of the invariant measure for (P-t)(t greater than or equal to 0).
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作者：Sowers, RB
作者单位：University of Southern California
摘要：In this paper we prove some intermittency-type estimates for the stochastic partial differential equation du = L u dt + M(1)u circle dW(t)(l), where L is a strongly elliptic second-order partial differential operator and the M(l)'s are first-order partial differential operators. Here the W-l's are standard Wiener processes and circle denotes Stratonovich integration. We assume for simplicity that u(0, .) equivalent to 1. Our interest here is the behavior of E[\ u(t, x)\(p)] for large time and ...
