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Mathematics: Recent submissions
Now showing items 281-300 of 462
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Rough path analysis via fractional calculus
(American Mathematical Society, 2009-11-02) -
Stochastic integral representation of the L2 modulus of Brownian local time and a central limit theorem
(Institute of Mathematical Statistics (IMS), 2009-11-09)The purpose of this note is to prove a central limit theorem for the L2-modulus of continuity of the Brownian local time obtained in [3], using techniques of stochastic analysis. The main ingredients of the proof are an ... -
Fractional martingales and characterization of the fractional Brownian motion
(Institute of Mathematical Statistics, 2009-11-19)In this paper we introduce the notion of fractional martingale as the fractional derivative of order α of a continuous local martingale, where α∈(−½, ½), and we show that it has a nonzero finite variation of order 2/(1+2α), ... -
Central limit theorem for the third moment in space of the Brownian local time increments
(Institute of Mathematical Statistics (IMS), 2010-09-14)The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic ... -
Limit theorems for nonlinear functionals of Volterra processes via white noise analysis
(Bernoulli Society for Mathematical Statistics and Probability, 2010-11-10)By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the ... -
Central and non-central limit theorems for weighted power variations of fractional Brownian motion
(Annals of the Institute Henri Poincaré, 2010-10-01)n this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional Brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central ... -
Feynman-Kac formula for the heat equation driven by fractional white noise
(Institute of Mathematical Statistics, 2011-02-01)We establish a version of the Feynman–Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process ... -
A construction of the rough path above fractional Brownian motion using Volterra’s representation
(Institute of Mathematical Statistics, 2011-09-01)This note is devoted to construct a rough path above a multidimensional fractional Brownian motion B with any Hurst parameter H∈(0, 1), by means of its representation as a Volterra Gaussian process. This approach yields ... -
Malliavin calculus for backward stochastic differential equations and applications to numerical solutions
(Institute of Mathematical Statistics, 2011-04-01)In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The ... -
Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter H < 1/2
(Institute of Mathematical Statistics, 2012-09-01)In this paper, a Feynman–Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H < 1/2. To establish ... -
Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II
(Institute of Mathematical Statistics (IMS), 2013-10-13)The purpose of this paper is to provide a complete description the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter H=1/6. -
Central limit theorem for an additive functional of the fractional Brownian motion
(Institute of Mathematical Statistics, 2014-01-09)We prove a central limit theorem for an additive functional of the d-dimensional fractional Brownian motion with Hurst index H∈(11+d,1d), using the method of moments, extending the result by Papanicolaou, Stroock and ... -
The Incidence Hopf Algebra of Graphs
(Society for Industrial and Applied Mathematics, 2012-05-03)The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite graphs, and whose Hopf product and coproduct admit simple combinatorial descriptions. ... -
About direct summands of projective modules over Laurent polynomial rings
(American Mathematical Society, 1991-08-01) -
On the continuation of an invariant torus in a family with rapid oscillations
(Society for Industrial and Applied Mathematics, 2000-01-01)A persistence theorem for attracting invariant tori for systems subjected to rapidly oscillating perturbations is proved. The singular nature of these perturbations prevents the direct application of the standard persistence ... -
Center manifolds for smooth invariant manifolds
(American Mathematical Society, 2000-06-27)We study dynamics of flows generated by smooth vector fields in Rn in the vicinity of an invariant and closed smooth manifold Y. By applying the Hadamard graph transform technique, we show that there exists an invariant ... -
Geometric Singular Perturbation Approach to Steady-State Poisson--Nernst--Planck Systems
(Society for Industrial and Applied Mathematics, 2005-01-05)Boundary value problems of a one-dimensional steady-state Poisson--Nernst--Planck (PNP) system for ion flow through a narrow membrane channel are studied. By assuming the ratio of the Debye length to a characteristic length ... -
Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges
(Society for Industrial and Applied Mathematics, 2007-02-01)Ionic channels and semiconductor devices use atomic scale structures to control macroscopic flows from one reservoir to another. The one‐dimensional steady‐state Poisson‐Nernst‐Planck (PNP) system is a useful representation ... -
Asymptotic Expansions of I-V Relations via a Poisson–Nernst–Planck System
(Society for Industrial and Applied Mathematics, 2008-01-01)We investigate higher order matched asymptotic expansions of a steady-state Poisson–Nernst–Planck (PNP) system with particular attention to the I-V relations of ion channels. Assuming that the Debye length is small relative ... -
Weak gravitational fields
(American Institute of Physics, 1974-01-01)We consider the set of Ck bounded tensor fields of type (r,s) on R 4 in the topology of uniform Ck convergence. For each k≥2, the map sending a metric to its curvature tensor is shown to be analytic at the Minkowski metric. ...