3期

最新文章

• Harmonic coordinates for diffusions in the plane AI翻译
  作者：Kersting, G
  摘要：For a class of diffusions X in the plane we construct a global system of coordinates u(x), such that u(x) is close to x at infinity and u(X) is a local martingale. Such coordinates are useful for the study of the long term behaviour of X. The construction uses probabilistic methods, in particular a coupling for general diffusions in the plane.
• Distance fluctuations and Lyapounov exponents AI翻译
  作者：Sznitman, AS
  摘要：We associate certain translation invariant random metrics on R(d) to Brownian motion evolving in a truncated Poissonian potential. These metrics behave over large distances, in an appropriate sense, like certain deterministic norms (the so-called Lyapounov exponents). We prove here upper bounds on the size of fluctuations of the metrics around their mean. Under an additional assumption of rotational invariance, we also derive upper bounds on the difference between the mean of the metrics and t...
• Majorizing measures: The generic chaining AI翻译
  作者：Talagrand, M
  作者单位：Sorbonne Universite
  摘要：Majorizing measures provide bounds for the supremum of stochastic processes. They represent the most general possible form of the chaining argument going back to Kolmogorov. Majorizing measures arose from the theory of Gaussian processes, but they now have applications far beyond this setting. The fundamental question is the construction of these measures. This paper focuses on the tools that have been developed for this purpose and, in particular, the use of geometric ideas. Applications are ...
• Random Fourier series and continuous additive functionals of Levy processes on the torus AI翻译
  作者：Marcus, MB; Rosen, J
  作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY)
  摘要：Let X be an exponentially killed Levy process on T-n, the n-dimensional torus, that satisfies a sector condition. (This includes symmetric Levy processes.) Let F-e denote the extended Dirichlet space of X. Let h is an element of F-e and let {h(y), y is an element of T-n} denote the set of translates of h. That is, h(y)(.) = h(. - y). We consider the family of zero-energy continuous additive functions {N-t([hy]), (y, t) is an element of T-n x R(+)} as defined by Fukushima. For a very large clas...
• Strong law of large numbers for sums of products AI翻译
  作者：Zhang, CH
  摘要：Let X, X(n), n greater than or equal to 1, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers for k = 2 without regularity conditions on X, [GRAPHICS] for k greater than or equal to 3 in three cases: (i) symmetric X, (ii) P{X greater than or equal to 0} = 1 and (iii) regularly varying P{\X\ > x} as x --> infinity, without further conditions, and for general X and k under a condition on the growt...
• Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation AI翻译
  作者：Horvath, L; Shao, QM
  作者单位：National University of Singapore
  摘要：Let {X(n), 1 less than or equal to n < infinity} be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index 0 < alpha < 2. The limit of x(n)(-1) log P{S-n/max \X(i)\ greater than or equal to x(n)} is found when x(n) --> infinity and x(n)/n --> 0. The large deviation result is used to prove the law of the iterated logarithm for the self-normalized partial sums.
• On the density of the maximum of smooth Gaussian processes AI翻译
  作者：Diebolt, J; Posse, C
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We obtain an integral formula for the density of the maximum of smooth Gaussian processes. This expression induces explicit nonasymptotic lower and upper bounds which are in general asymptotic to the density. Moreover, these bounds allow us to derive simple asymptotic formulas for the density with rate of approximation as well as accurate asymptotic bounds. In particular, in the case of stationary processes, the latter upper bound improves the well-known bound based on Rice's formula. In the c...
• Gaussian chaos and sample path properties of additive functionals of symmetric Markov processes AI翻译
  作者：Marcus, MB; Rosen, J
  作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY)
  摘要：Let X be a strongly symmetric Hunt process with alpha-potential density u(alpha)(x, y). Let G(alpha)(2) = {mu\integral integral(u(alpha)(x, y))(2) d mu(x)d mu(y) < infinity} and let L(t)(mu) denote the continuous additive functional with Revuz measure mu. For a set of positive measures M subset of G(alpha)(2), subject to some additional regularity conditions, we consider families of continuous (in time) additive functionals L = {L(t)(mu), (t, mu) is an element of R(+) X M} of X and a second-or...
• A note on exact convergence rates in some martingale central limit theorems AI翻译
  作者：Renz, J
  作者单位：Michigan State University
  摘要：Bolthausen established a bound of order 1/root n on the rate of convergence in the central limit theorem for martingale difference arrays having bounded conditional moments of order 4. In the present paper it is shown how much this moment condition can be relaxed while maintaining the same rate of convergence. An example shows that, unlike in the i.i.d. case, a moment condition of order 3 is not enough. Furthermore, exact rates of convergence are derived for moment conditions of order between ...
• The complete convergence theorem of the contact process on trees AI翻译
  作者：Zhang, Y
  摘要：Consider the contact process on a homogeneous tree with degree d greater than or equal to 3. Denote by lambda(c) = inf{lambda:P(o is an element of xi i.o.) > 0} the critical value of local survival probability, where o is the root of the tree. Pemantle and Durrett and Schinazi both conjectured that the complete convergence theorem should hold if lambda > lambda(c). Here we answer the conjecture affirmatively. Furthermore, we will show that P(o is an element of xi(t)(o) i.o.) = 0 at lambda(c). ...