Probability Theory and Related Fields

最新文章

• THE UNIFORM RANDOM TREE IN A BROWNIAN EXCURSION AI翻译
  作者：LEGALL, JF
  摘要：To any Brownian excursion e with duration sigma(e) and any t1, ..., t(p) is-an-element-of[0, sigma(e)], we associate a branching tree with p branches denoted by T(p)(e, t1, ..., t(p)), which is closely related to the structure of the minima of e. Our main theorem states that, if e is chosen according to the Ito measure and (t1, ..., t(p)) according to Lebesgue measure on [0, sigma(e)]p, the tree T(p)(e, t1, ..., t(p)) is distributed according to the uniform measure on the set of trees with p b...
• PATH INTEGRAL FORMULAS FOR HEAT KERNELS AND THEIR DERIVATIVES AI翻译
  作者：NORRIS, JR
  摘要：The heat kernel and its derivatives of a vector Laplacian on the sections of a bundle over a compact Riemannian manifold are expressed as products of the scalar heat kernel of the manifold and path integrals over the Brownian bridge. The small-time asymptotics of these integrals are computed.
• RATES OF CLUSTERING IN STRASSENS LIL FOR PARTIAL SUM PROCESSES AI翻译
  作者：EINMAHL, U; MASON, DM
  作者单位：University of Delaware
  摘要：We provide a detailed description of the rate of clustering in Strassen's functional law of the iterated logarithm for partial sum processes. Necessary and sufficient conditions are given for certain clustering rates in terms of moment-type conditions. In the process, we also derive a new strong approximation of sums of iid random variables by a Wiener process.
• QUANTUM AND NONCAUSAL STOCHASTIC CALCULUS AI翻译
  作者：LINDSAY, JM
  摘要：The quantum stochastic calculus initiated by Hudson and Parthasarathy, and the non-causal stochastic calculus originating with the papers of Hitsuda and Skorohod, are two potent extensions of the Ito calculus, currently enjoying intensive development. The former provides a quantum probabilistic extension of Schrodinger's equation, enabling the construction of a Markov process for a quantum dynamical semigroup. The latter allows the treatment of stochastic differential equations which involve t...
• EXISTENCE AND UNIQUENESS OF SEMIMARTINGALE REFLECTING BROWNIAN MOTIONS IN AN ORTHANT AI翻译
  作者：TAYLOR, LM; WILLIAMS, RJ
  作者单位：University of California System; University of California San Diego
  摘要：This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of R(d). Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d - 1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in ...
• PREDICTABILITY AND STOPPING ON LATTICES OF SETS AI翻译
  作者：IVANOFF, BG; MERZBACH, E; SCHIOPUKRATINA, I
  作者单位：Bar Ilan University
  摘要：As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable sigma-algebra in terms of adapted and ''left-continuous'' processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable sigma-algebra can be ...
• NONEXPONENTIAL DECREASE OF THE HEAT KERNEL AI翻译
  作者：FLORCHINGER, P; LEANDRE, R
  作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Inria
  摘要：In this paper, we give estimates on the heat kernel on the diagonal in terms of exp [ - \Log t\alpha], alpha > 1 when t vanishes. Moreover, we compute, by means of the stochastic calculus of variations, the decay of the flatness of some heat kernels. On the other hand, we show that the computations in both cases are very similar.
• SELF-SIMILAR RANDOM MEASURES ARE LOCALLY SCALE-INVARIANT AI翻译
  作者：PATZSCHKE, N; ZAHLE, M
  摘要：In an earlier paper Patzschke and U. Zahle [11] have proved the existence of a fractional tangent measure at the typical point of a self-similar random measure Phi under rather special technical assumptions. In the present paper we remove the most restrictive one. Here we suppose the open set condition for the similarities, a constant positive lower bound for the random contraction ratios, and vanishing Phi on the boundary of the open set with probability 1. The tangent measure is D-scale-inva...
• HIERARCHIES OF HIGHER-ORDER KERNELS AI翻译
  作者：BERLINET, A
  摘要：Recent literature on functional estimation has shown the importance of kernels with vanishing moments although no general framework was given to build kernels of increasing order apart from some specific methods based on moment relationships. The purpose of the present paper is to develop such a framework and to show how to build higher order kernels with nice properties and to solve optimization problems about kernels. The proofs given here, unlike standard variational arguments, explain why ...
• A CLASS OF PATH-VALUED MARKOV-PROCESSES AND ITS APPLICATIONS TO SUPERPROCESSES AI翻译
  作者：LEGALL, JF
  摘要：Let (xi(S)) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with (xi(S)), which is closely related to the so-called superprocess with spatial motion (xi(S)). In particular, a subset H of the state space of (xi(S)) intersects the range of the superprocess if and only if the set of paths that hit H is not polar for the path-valued process. The latter property can be investigated using the tools of the potential...