2004

最新文章

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm AI翻译
  作者：Bass, RF; Chen, X
  作者单位：University of Connecticut; University of Tennessee System; University of Tennessee Knoxville
  摘要：If beta(t). is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee(gammabeta1) is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for beta(1) and -beta(1). We establish lim sup and lim inf laws of the iterated logarithm for beta(t) as t --> infinity.
• Euclidean Gibbs measures on loop lattices: Existence and a priori estimates AI翻译
  作者：Albeverio, S; Kondratiev, Y; Pasurek, T; Röckner, M
  作者单位：University of Bonn; University of Bielefeld; University of Bielefeld
  摘要：We present a new method to prove existence and uniform a priori estimates for Euclidean Gibbs measures corresponding to quantum anharmonic crystals. It is based first on the alternative characterization of Gibbs measures in terms of their logarithmic derivatives through integration by parts formulas, and second on the choice of appropriate Lyapunov functionals.
• A stochastic representation theorem with applications to optimization and obstacle problems AI翻译
  作者：Bank, P; El Karoui, N
  作者单位：Humboldt University of Berlin; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
  摘要：We study a new type of representation problem for optional processes with connections to singular control, optimal stopping and dynamic allocation problems. As an application, we show how to solve a variant of Skorohod's obstacle problem in the context of backward stochastic differential equations.
• Moderate deviations for diffusions with Brownian potentials AI翻译
  作者：Hu, YY; Shi, Z
  作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
  摘要：We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine tools in stochastic calculus, including Kotani's lemma and Lamperti's representation for exponential functionals. In particular, our result for quenched moderate deviations is in agreement with a recent theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 571-609] who studied the corresponding proble...
• The shattering dimension of sets of linear functionals AI翻译
  作者：Mendelson, S; Schechtman, G
  作者单位：Australian National University; Weizmann Institute of Science
  摘要：We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization techniques and tail estimates of norms, viewed as random variables on Euclidean spheres. The estimates of shattering dimensions can be applied to obtain error bounds for certain classes of functions, a fact which was the original motivation of this study. Althoug...
• Utility maximizing entropy and the second law of thermodynamics AI翻译
  作者：Slomczynski, W; Zastawniak, T
  作者单位：Jagiellonian University; University of Hull
  摘要：Expected utility maximization problems in mathematical finance lead to a generalization of the classical definition of entropy. It is demonstrated that a necessary and sufficient condition for the second law of thermodynamics to operate is that any one of the generalized entropies should tend to its minimum value of zero.
• Large deviations for random walk in random environment with holding times AI翻译
  作者：Dembo, A; Gantert, N; Zeitouni, O
  作者单位：Stanford University; Stanford University; Technion Israel Institute of Technology; Technion Israel Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities; Helmholtz Association; Karlsruhe Institute of Technology
  摘要：Suppose that the integers are assigned the random variables {w(x), mu(x)} (taking values in the unit interval times the space of probability measures on R+), which serve as an environment. This environment defines a random walk {X-t} (called a RWREH) which, when at x, waits a random time distributed according to mu(x) and then, after one unit of time, moves one step to the right with probability omega(x), and one step to the left with probability 1 - omega(x). We prove large deviation principl...
• Occupation densities for SPDEs with reflection AI翻译
  作者：Zambotti, L
  作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
  摘要：We consider the solution (u, eta) of the white-noise driven stochastic partial differential equation with reflection on the space interval [0, 1] introduced by Nualart and Pardoux, where eta is a reflecting measure on [0, infinity) x (0, 1) which forces the continuous function u, defined on [0, infinity) x [0, 1], to remain nonnegative and eta has support in the set of zeros of u. First, we prove that at any fixed time t > 0, the measure eta([0, t] x dtheta) is absolutely continuous w.r.t. the...
• Weak Poincare inequalities on domains defined by brownian rough paths AI翻译
  作者：Aida, S
  作者单位：University of Osaka
  摘要：We prove weak Poincare inequalities on domains which are inverse images of open sets in Wiener spaces under continuous functions of Brownian rough paths. The result is applicable to Dirichlet forms on loop groups and connected open subsets of path spaces over compact Riemannian manifolds.
• Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients AI翻译
  作者：Delarue, F
  作者单位：Universite Paris Cite
  摘要：We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward-backward stochastic differential equations and introduce the new concept of auxiliary SDEs.