Nonlinear Analysis, Theory, Methods and Applications, ISSN 0362-546X, 06/2016, Volume 138, pp. 83 - 92

This mostly expository paper shows how weak convergence methods provide simple, elegant proofs of (i) the stabilization of an inverted pendulum under fast...

Weak convergence | Stabilization | Adiabatic invariance

Weak convergence | Stabilization | Adiabatic invariance

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 07/2015, Volume 63, Issue 13, pp. 3522 - 3536

We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting...

hidden models | Government | Channel estimation | Markov processes | Time measurement | Approximation methods | Approximate nonlinear filtering | {\cal C} -weak convergence | stochastic processes | partially observable systems | Convergence | {\cal C}-weak convergence | C-weak convergence | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Stochastic processes | Analysis | Least squares | Electric filters | Approximation theory | Research

hidden models | Government | Channel estimation | Markov processes | Time measurement | Approximation methods | Approximate nonlinear filtering | {\cal C} -weak convergence | stochastic processes | partially observable systems | Convergence | {\cal C}-weak convergence | C-weak convergence | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Stochastic processes | Analysis | Least squares | Electric filters | Approximation theory | Research

Journal Article

Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 10, pp. 2711 - 2720

In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in...

Strong and weak convergence theorems | Nonexpansive mapping | Fixed point | strong and weak convergence theorems | MATHEMATICS | MATHEMATICS, APPLIED | nonexpansive mapping | WEAK-CONVERGENCE

Strong and weak convergence theorems | Nonexpansive mapping | Fixed point | strong and weak convergence theorems | MATHEMATICS | MATHEMATICS, APPLIED | nonexpansive mapping | WEAK-CONVERGENCE

Journal Article

Electronic journal of statistics, ISSN 1935-7524, 2016, Volume 10, Issue 1, pp. 1181 - 1222

The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the...

6 Data source | quasi-Hadamard differentiability | statistical functional | functional delta-method | 2 International | weak convergence for the open-ball sigma-algebra | Bootstrap | Quasi-Hadamard differentiability | Statistical functional | Weak convergence for the open-ball σ-algebra | Functional delta-method | EMPIRICAL PROCESSES | SEQUENCES | RISK FUNCTIONALS | STATISTICS & PROBABILITY | DEPENDENT DATA | STATIONARY OBSERVATIONS | U-STATISTICS | WEAK-CONVERGENCE | NONSEPARABLE METRIC-SPACES | V-STATISTICS | BLOCKWISE BOOTSTRAP

6 Data source | quasi-Hadamard differentiability | statistical functional | functional delta-method | 2 International | weak convergence for the open-ball sigma-algebra | Bootstrap | Quasi-Hadamard differentiability | Statistical functional | Weak convergence for the open-ball σ-algebra | Functional delta-method | EMPIRICAL PROCESSES | SEQUENCES | RISK FUNCTIONALS | STATISTICS & PROBABILITY | DEPENDENT DATA | STATIONARY OBSERVATIONS | U-STATISTICS | WEAK-CONVERGENCE | NONSEPARABLE METRIC-SPACES | V-STATISTICS | BLOCKWISE BOOTSTRAP

Journal Article

Quantitative finance, ISSN 1469-7696, 2009, Volume 10, Issue 2, pp. 177 - 194

Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative,...

Weak convergence | Boundary behaviour | Strong convergence | Discretization | CEV process | Square root process | Stochastic volatility | Euler-Maruyama | Heston | Cev process | Euler-maruyama | BUSINESS, FINANCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | Stochastic volatility; Heston; Square root process; CEV process; Euler-Maruyama; Discretization; Strong convergence; Weak convergence; Boundary behaviour

Weak convergence | Boundary behaviour | Strong convergence | Discretization | CEV process | Square root process | Stochastic volatility | Euler-Maruyama | Heston | Cev process | Euler-maruyama | BUSINESS, FINANCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | Stochastic volatility; Heston; Square root process; CEV process; Euler-Maruyama; Discretization; Strong convergence; Weak convergence; Boundary behaviour

Journal Article

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2012, Volume 18, Issue 3, pp. 764 - 782

Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are...

Copula functions | Central limit theorem | Second order partial derivatives | Coordinate systems | Trajectories | Logarithms | First order partial derivatives | Statistics | Partial derivatives | Distribution functions | Multiplier central limit theorem | Weak convergence | Empirical process | Archimedean copula | Empirical copula | Tail dependence | Gaussian copula | Extreme-value copula | Brownian bridge | TESTS | empirical process | STATISTICS & PROBABILITY | tail dependence | DEPENDENCE | DISTRIBUTIONS | empirical copula | INDEPENDENCE | extreme-value copula | WEAK-CONVERGENCE | multiplier central limit theorem | weak convergence

Copula functions | Central limit theorem | Second order partial derivatives | Coordinate systems | Trajectories | Logarithms | First order partial derivatives | Statistics | Partial derivatives | Distribution functions | Multiplier central limit theorem | Weak convergence | Empirical process | Archimedean copula | Empirical copula | Tail dependence | Gaussian copula | Extreme-value copula | Brownian bridge | TESTS | empirical process | STATISTICS & PROBABILITY | tail dependence | DEPENDENCE | DISTRIBUTIONS | empirical copula | INDEPENDENCE | extreme-value copula | WEAK-CONVERGENCE | multiplier central limit theorem | weak convergence

Journal Article

Queueing systems, ISSN 1572-9443, 2018, Volume 91, Issue 1-2, pp. 15 - 47

We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL) in discrete time, which complements the sample-path and stationary...

60F25 | Systems Theory, Control | Periodic queues | Probability Theory and Stochastic Processes | L = \lambda W$$ L = λ W | 90B22 | Emergency departments | Business and Management | Central limit theorem | Operations Research/Decision Theory | Little’s law | Weak convergence in $$(\ell _1)^d$$ ( ℓ 1 ) d | Supply Chain Management | 60K25 | Computer Communication Networks | 60F05 | L= λW | Weak convergence in (l | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Weak convergence in (l1)(d) | L =lambda W | Little's law | Laws, regulations and rules | Analysis | Management science | Emergency services | Data analysis | Theorems | Emergency medical services

60F25 | Systems Theory, Control | Periodic queues | Probability Theory and Stochastic Processes | L = \lambda W$$ L = λ W | 90B22 | Emergency departments | Business and Management | Central limit theorem | Operations Research/Decision Theory | Little’s law | Weak convergence in $$(\ell _1)^d$$ ( ℓ 1 ) d | Supply Chain Management | 60K25 | Computer Communication Networks | 60F05 | L= λW | Weak convergence in (l | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Weak convergence in (l1)(d) | L =lambda W | Little's law | Laws, regulations and rules | Analysis | Management science | Emergency services | Data analysis | Theorems | Emergency medical services

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 05/2016, Volume 45, Issue 10, pp. 2834 - 2841

In this paper we show an approximation in law to the subfractional Brownian motion with in the Skorohod topology. The construction of these approximations is...

Weak convergence | Subfractional Brownian motion | Random walks | Fractional Brownian motion | Subfractional Brownian motion;Weak convergence | RESPECT | WEAK-CONVERGENCE | STATISTICS & PROBABILITY | Brownian movements | Random walk theory | Brownian motion | Construction | Approximation | Mathematical analysis | Random walk | Images | Topology | Statistics

Weak convergence | Subfractional Brownian motion | Random walks | Fractional Brownian motion | Subfractional Brownian motion;Weak convergence | RESPECT | WEAK-CONVERGENCE | STATISTICS & PROBABILITY | Brownian movements | Random walk theory | Brownian motion | Construction | Approximation | Mathematical analysis | Random walk | Images | Topology | Statistics

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 09/2019, Volume 173, pp. 704 - 723

A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the...

Empirical beta copula | Empirical checkerboard copula | Delete-[formula omitted] jackknife | Weighted weak convergence | Rank-based inference | SEMIPARAMETRIC ESTIMATION | BERNSTEIN COPULA | APPROXIMATIONS | BEHAVIOR | STATISTICS & PROBABILITY | PARAMETERS | Delete-h jackknife | NONPARAMETRIC-ESTIMATION | WEAK-CONVERGENCE | Statistics | Mathematics

Empirical beta copula | Empirical checkerboard copula | Delete-[formula omitted] jackknife | Weighted weak convergence | Rank-based inference | SEMIPARAMETRIC ESTIMATION | BERNSTEIN COPULA | APPROXIMATIONS | BEHAVIOR | STATISTICS & PROBABILITY | PARAMETERS | Delete-h jackknife | NONPARAMETRIC-ESTIMATION | WEAK-CONVERGENCE | Statistics | Mathematics

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2008, Volume 56, Issue 10, pp. 2572 - 2579

By using the concept of △ -convergence introduced by Lim [T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976) 179–182], we are...

Weak convergence | [formula omitted]-convergence | Fixed points | Nonexpansive mappings | CAT spaces | convergence | Analogs | Theorems | Approximation | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Weak convergence | [formula omitted]-convergence | Fixed points | Nonexpansive mappings | CAT spaces | convergence | Analogs | Theorems | Approximation | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Journal Article

Journal of multivariate analysis, ISSN 0047-259X, 2019, Volume 171, pp. 139 - 162

This paper is concerned with modeling the dependence structure of two (or more) time series in the presence of a (possibly multivariate) covariate which may...

Weak convergence | Asymptotic representation | Nonparametric SCOMDY model | Empirical copula process | CHARN model | Nonparametric AR-ARCH model | Goodness-of-fit testing | CONDITIONAL COPULA | ERROR DISTRIBUTION | SEMIPARAMETRIC ESTIMATION | TESTS | STATISTICS & PROBABILITY | WEAK-CONVERGENCE

Weak convergence | Asymptotic representation | Nonparametric SCOMDY model | Empirical copula process | CHARN model | Nonparametric AR-ARCH model | Goodness-of-fit testing | CONDITIONAL COPULA | ERROR DISTRIBUTION | SEMIPARAMETRIC ESTIMATION | TESTS | STATISTICS & PROBABILITY | WEAK-CONVERGENCE

Journal Article

Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, 8/2017, Volume 69, Issue 4, pp. 833 - 864

A test procedure based on continuous observation to detect a change in drift parameters of an ergodic diffusion process is proposed. The asymptotic behavior of...

Statistics, general | Statistics | Weak convergences in $$L^2(0 , 1)$$ L 2 ( 0 , 1 ) | Change point problems | Diffusion processes | Weak convergences in L | 0 , 1 | Weak convergences in L-2(0,1) | STATISTICS & PROBABILITY | PARAMETERS | Economic models | Null hypothesis | Asymptotic properties | Change detection | Ergodic processes

Statistics, general | Statistics | Weak convergences in $$L^2(0 , 1)$$ L 2 ( 0 , 1 ) | Change point problems | Diffusion processes | Weak convergences in L | 0 , 1 | Weak convergences in L-2(0,1) | STATISTICS & PROBABILITY | PARAMETERS | Economic models | Null hypothesis | Asymptotic properties | Change detection | Ergodic processes

Journal Article

Bernoulli, ISSN 1350-7265, 05/2017, Volume 23, Issue 2, pp. 1233 - 1278

Let (X-1, xi(1)), (X-2, xi(2)),... be i.i.d. copies of a pair (X, xi) where X is a random process with paths in the Skorokhod space D[0, infinity) and xi is a...

Renewal theory | Random process with immigration | Weak convergence of finite-dimensional distributions | Shot noise processes | SHOT-NOISE PROCESSES | RATES | NUMBER | random process with immigration | shot noise processes | MODELS | renewal theory | WEAK-CONVERGENCE | STATISTICS & PROBABILITY | EMPTY BOXES | weak convergence of finite-dimensional distributions | RENEWAL THEOREM

Renewal theory | Random process with immigration | Weak convergence of finite-dimensional distributions | Shot noise processes | SHOT-NOISE PROCESSES | RATES | NUMBER | random process with immigration | shot noise processes | MODELS | renewal theory | WEAK-CONVERGENCE | STATISTICS & PROBABILITY | EMPTY BOXES | weak convergence of finite-dimensional distributions | RENEWAL THEOREM

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2008, Volume 68, Issue 12, pp. 3689 - 3696

A CAT(0) space is a geodesic space for which each geodesic triangle is at least as ‘thin’ as its comparison triangle in the Euclidean plane. A notion of...

Weak convergence | [formula omitted]-convergence | Fixed points | CAT spaces | Δ-convergence | MATHEMATICS | MATHEMATICS, APPLIED | Delta-convergence | fixed points | BANACH-SPACES | MAPPINGS | FIXED-POINT PROPERTY | weak convergence

Weak convergence | [formula omitted]-convergence | Fixed points | CAT spaces | Δ-convergence | MATHEMATICS | MATHEMATICS, APPLIED | Delta-convergence | fixed points | BANACH-SPACES | MAPPINGS | FIXED-POINT PROPERTY | weak convergence

Journal Article

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1812, 2013, Volume 2013, Issue 1, pp. 1 - 10

We introduce a new iterative process which can be seen as a hybrid of Picard and Mann iterative processes. We show that the new process converges faster than...

Mathematical and Computational Biology | rate of convergence | nonexpansive mapping | Mathematics | Topology | iterative process | strong convergence | fixed point | Analysis | Mathematics, general | contraction | Applications of Mathematics | Differential Geometry | weak convergence | Weak convergence | Strong convergence | Iterative process | Rate of convergence | Contraction | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | WEAK-CONVERGENCE | APPROXIMATING FIXED-POINTS | Fixed point theory | Usage | Banach spaces | Iterative methods (Mathematics) | Contraction operators

Mathematical and Computational Biology | rate of convergence | nonexpansive mapping | Mathematics | Topology | iterative process | strong convergence | fixed point | Analysis | Mathematics, general | contraction | Applications of Mathematics | Differential Geometry | weak convergence | Weak convergence | Strong convergence | Iterative process | Rate of convergence | Contraction | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | WEAK-CONVERGENCE | APPROXIMATING FIXED-POINTS | Fixed point theory | Usage | Banach spaces | Iterative methods (Mathematics) | Contraction operators

Journal Article

Stochastic processes and their applications, ISSN 0304-4149, 2008, Volume 118, Issue 4, pp. 614 - 628

We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order...

Weak convergence | Limit theorems | Multiple stochastic integrals | Malliavin calculus | Gaussian processes | multiple stochastic integrals | STATISTICS & PROBABILITY | limit theorems | weak convergence | Multiple stochastic integrals Limit theorems Gaussian processes Malliavin calculus Weak convergence

Weak convergence | Limit theorems | Multiple stochastic integrals | Malliavin calculus | Gaussian processes | multiple stochastic integrals | STATISTICS & PROBABILITY | limit theorems | weak convergence | Multiple stochastic integrals Limit theorems Gaussian processes Malliavin calculus Weak convergence

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2017, Volume 263, Issue 5, pp. 3110 - 3146

In this paper, we establish the Freidlin–Wentzell's large deviations for 3D stochastic primitive equations with small noise perturbation. The weak convergence...

Weak convergence method | Primitive equation | Large deviations | LARGE-SCALE OCEAN | MATHEMATICS | NOISE | GLOBAL WELL-POSEDNESS | ATMOSPHERE

Weak convergence method | Primitive equation | Large deviations | LARGE-SCALE OCEAN | MATHEMATICS | NOISE | GLOBAL WELL-POSEDNESS | ATMOSPHERE

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 2016, Volume 21

We prove general results about separation and weak (#) - convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More...

Separating | Le Cam theorem | Vague convergence | Convergence determining | Weak#-convergence of measures | Boundedly finite measure | Stone-Weierstrass | boundedly finite measure | R-TREES | METRIC MEASURE-SPACES | STATISTICS & PROBABILITY | convergence determining | vague convergence separating | weak (#) convergence of measures | Mathematics - Probability

Separating | Le Cam theorem | Vague convergence | Convergence determining | Weak#-convergence of measures | Boundedly finite measure | Stone-Weierstrass | boundedly finite measure | R-TREES | METRIC MEASURE-SPACES | STATISTICS & PROBABILITY | convergence determining | vague convergence separating | weak (#) convergence of measures | Mathematics - Probability

Journal Article

Carpathian Journal of Mathematics, ISSN 1584-2851, 2019, Volume 35, Issue 3, pp. 293 - 304

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, presented here for the first time, we introduce and study the class...

Krasoselskij iteration | MATHEMATICS, APPLIED | enriched nonexpansive mapping | ERGODIC-THEOREMS | EQUATIONS | ALGORITHMS | strong convergence | MATHEMATICS | NONLINEAR MAPPINGS | CONVERGENCE THEOREMS | fixed point | PRODUCT | WEAK-CONVERGENCE | CONSTRUCTION | weak convergence | OPERATORS

Krasoselskij iteration | MATHEMATICS, APPLIED | enriched nonexpansive mapping | ERGODIC-THEOREMS | EQUATIONS | ALGORITHMS | strong convergence | MATHEMATICS | NONLINEAR MAPPINGS | CONVERGENCE THEOREMS | fixed point | PRODUCT | WEAK-CONVERGENCE | CONSTRUCTION | weak convergence | OPERATORS

Journal Article

Journal of theoretical probability, ISSN 1572-9230, 2018, Volume 32, Issue 3, pp. 1145 - 1165

The consistency of a bootstrap or resampling scheme is classically validated by weak convergence of conditional laws. However, when working with stochastic...

Confidence intervals | Weak convergence | 62G09 | Stochastic processes | 62E20 | Probability Theory and Stochastic Processes | Bootstrap | Mathematics | Conditional weak convergence | Statistics, general | Resampling | TESTS | STATISTICS & PROBABILITY | Convergence (Social sciences)

Confidence intervals | Weak convergence | 62G09 | Stochastic processes | 62E20 | Probability Theory and Stochastic Processes | Bootstrap | Mathematics | Conditional weak convergence | Statistics, general | Resampling | TESTS | STATISTICS & PROBABILITY | Convergence (Social sciences)

Journal Article

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