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Parameter Estimation and Model Testing for Markov Processes via Conditional Characteristic Functions
Conditional characteristic function Diffusion processes Empirical likelihood Kernel smoothing L′ evy driven processes
2016/1/19
Markov processes are used in a wide range of disciplines including finance.The transition densities of these processes are often unknown. However, the conditionalcharacteristic functions are more like...
Structured and Simultaneous Lyapunov Functions for System Stability Problems
Structured Simultaneous Lyapunov Functions System Stability Problems
2015/7/13
It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of dx/dt...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
polynomial-time algorithm determining quadratic Lyapunov functions nonlinear systems
2015/7/13
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
In this paper we introduce a control policy which we refer to as the iterated approximate value function policy. The generation of this policy requires two stages, the first one carried out off-line, ...
PROXIMAL NEWTON-TYPE METHODS FOR MINIMIZING COMPOSITE FUNCTIONS
convex optimization nonsmooth optimization
2015/7/3
We generalize Newton-type methods for minimizing smooth functions to handle a
sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping.
Rational hypergeometric functions
Multivariate hypergeometric function complex curved surface the double circular orbit closures geometric function
2014/12/29
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors project...
Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
Walter's function nonlinear schrodinger equation periodic vector lattice
2014/12/29
In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödi...
Rabi switch of condensate wave functions in a multicomponent Bose gas
Coupling bose-einstein condensate the wave function the electromagnetic field
2014/12/25
Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wave function of ...
Ruelle-Lanford functions for quantum spin systems
Macro expectations and quantum gibbs a classic case of cluster expansion assignment operator quantum unified quantum
2014/12/24
We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions [20, 34] and direct subaddit...
The Structure of Bivariate Rational Hypergeometric Functions
Codimension 2 lattice structure configuration rational function F partial derivatives zero complex curved surface
2014/12/24
We describe the structure of all codimension-2 lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all the partial derivatives of which are ...
When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs
bootstrap copula epigraph hypograph stable tail dependence function minimum distance estimation weak convergence
2013/6/14
For copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube, the empirical copula process does not converge weakly with respect to the supremum distance. This ...
Adaptive confidence intervals for regression functions under shape constraints
Adaptation confidence interval convex function coverage probability expected length minimax estimation modulus of continuity monotone func-tion nonparametric regression shape constraint white noise model
2013/6/14
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of conf...
Evolution of Covariance Functions for Gaussian Process Regression using Genetic Programming
Gaussian Process Genetic Programming Structure Identification
2013/6/14
In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based...
Optimization with First-Order Surrogate Functions
Optimization First-Order Surrogate Functions
2013/6/14
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we mak...
On the Generalization Ability of Online Learning Algorithms for Pairwise Loss Functions
Generalization Ability Online Learning Algorithms Pairwise Loss Functions
2013/6/14
In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample...