2011, ISBN 0199575312, Volume 9780199575312, xii, 652

.... However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation procedures...

Markov processes | Population | Statistical methods | applied mathematics | Even-time pairs | Probability equations | Stochastic realizations | Approximation | Random processes

Markov processes | Population | Statistical methods | applied mathematics | Even-time pairs | Probability equations | Stochastic realizations | Approximation | Random processes

Book

2014, De Gruyter studies in mathematics, ISBN 9783110329674, Volume 56, 57., 2 v.

Book

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 07/2012, Volume 229-232, pp. 1 - 12

â–º Sparse grid integration function evaluations to Fourier coefficients. â–º Sparse pseudospectral approximation superior to nonintrusive spectral projection...

Non-intrusive spectral projection | Uncertainty quantification | Sparse grids | Polynomial chaos | Stochastic collocation | Pseudospectral methods | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | STOCHASTIC COLLOCATION METHOD | ENGINEERING, MULTIDISCIPLINARY | INTEGRATION | PARTIAL-DIFFERENTIAL-EQUATIONS | QUADRATURE | Tensors | Sensitivity analysis | Numerical integration | Approximation | Computer simulation | Mathematical analysis | Mathematical models | Three dimensional | Mathematics - Numerical Analysis

Non-intrusive spectral projection | Uncertainty quantification | Sparse grids | Polynomial chaos | Stochastic collocation | Pseudospectral methods | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | STOCHASTIC COLLOCATION METHOD | ENGINEERING, MULTIDISCIPLINARY | INTEGRATION | PARTIAL-DIFFERENTIAL-EQUATIONS | QUADRATURE | Tensors | Sensitivity analysis | Numerical integration | Approximation | Computer simulation | Mathematical analysis | Mathematical models | Three dimensional | Mathematics - Numerical Analysis

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2017, Volume 50, Issue 9, pp. 1 - 60

.... Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods...

chemical master equation | inference methods | stochastic simulations | chemical reaction networks | stochastic chemical kinetics | Bayesian inference | approximation methods | MASTER-EQUATION | PHYSICS, MULTIDISCIPLINARY | COMPLEX CHEMICAL-REACTIONS | DIFFERENTIAL-EQUATIONS | SIMULATION | PHYSICS, MATHEMATICAL | MARKOV JUMP-PROCESSES | STEADY-STATE APPROXIMATION | REACTION NETWORKS | FAST VARIABLES | LINEAR NOISE APPROXIMATION | BAYESIAN-INFERENCE

chemical master equation | inference methods | stochastic simulations | chemical reaction networks | stochastic chemical kinetics | Bayesian inference | approximation methods | MASTER-EQUATION | PHYSICS, MULTIDISCIPLINARY | COMPLEX CHEMICAL-REACTIONS | DIFFERENTIAL-EQUATIONS | SIMULATION | PHYSICS, MATHEMATICAL | MARKOV JUMP-PROCESSES | STEADY-STATE APPROXIMATION | REACTION NETWORKS | FAST VARIABLES | LINEAR NOISE APPROXIMATION | BAYESIAN-INFERENCE

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2018, Volume 171, Issue 1, pp. 217 - 282

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty...

Theoretical, Mathematical and Computational Physics | Sample average approximation of stochastic optimization | Mathematics | Portfolio allocation | 90C15 | Goodness-of-fit testing | Conic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C47 | 90C25 | Numerical Analysis | Distributionally robust optimization | 90C34 | Inventory management | 62G10 | Combinatorics | Data-driven optimization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RISK | Economic models | Approximation | Robustness (mathematics) | Asymptotic properties | Mathematical analysis | Decision making | Asymptotic methods | Monte Carlo simulation | Optimization | Goodness of fit

Theoretical, Mathematical and Computational Physics | Sample average approximation of stochastic optimization | Mathematics | Portfolio allocation | 90C15 | Goodness-of-fit testing | Conic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C47 | 90C25 | Numerical Analysis | Distributionally robust optimization | 90C34 | Inventory management | 62G10 | Combinatorics | Data-driven optimization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RISK | Economic models | Approximation | Robustness (mathematics) | Asymptotic properties | Mathematical analysis | Decision making | Asymptotic methods | Monte Carlo simulation | Optimization | Goodness of fit

Journal Article

1981, ISBN 9783540108634, Volume 879, 104

Book

2019, Springer Optimization and Its Applications, ISBN 9783030127664, Volume 145, 244

This book focuses on the development of approximation-related algorithms and their relevant applications...

Approximation algorithms | Approximations and Expansions | Probability Theory and Stochastic Processes | Mathematics | Algorithms | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis

Approximation algorithms | Approximations and Expansions | Probability Theory and Stochastic Processes | Mathematics | Algorithms | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis

eBook

IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 05/2020, Volume 31, Issue 5, pp. 1602 - 1615

This paper deals with iterative Jacobian-based recursion technique for the root-finding problem of the vector-valued function, whose evaluations are...

root finding | Estimation | noisy function measurements | Newtonâ€™s method | Noise measurement | Covariance matrices | Optimization | Rosenbrock function | Convergence | stochastic optimization | Jacobian matrices | stochastic approximation (SA) | Gradient descent | variance reduction | Approximation algorithms | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHM | PID CONTROLLER | GRADIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | NEURAL-NETWORKS | Newton's method | COMPUTER SCIENCE, THEORY & METHODS

root finding | Estimation | noisy function measurements | Newtonâ€™s method | Noise measurement | Covariance matrices | Optimization | Rosenbrock function | Convergence | stochastic optimization | Jacobian matrices | stochastic approximation (SA) | Gradient descent | variance reduction | Approximation algorithms | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHM | PID CONTROLLER | GRADIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | NEURAL-NETWORKS | Newton's method | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

9.
Full Text
Analysis and Approximation of Rare Events

: Representations and Weak Convergence Methods

2019, Probability Theory and Stochastic Modelling, ISBN 9781493995776, Volume 94, 577

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A...

Approximation theory | Probability Theory and Stochastic Processes | Mathematics | Numerical Analysis | Mathematical and Computational Engineering

Approximation theory | Probability Theory and Stochastic Processes | Mathematics | Numerical Analysis | Mathematical and Computational Engineering

eBook

Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 8, pp. 3015 - 3034

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e...

Uncertainty quantification | Polynomial chaos | Sparse approximation | Compressive sampling | Stochastic PDE | RECONSTRUCTION | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | ATOMIC DECOMPOSITION | PHYSICS, MATHEMATICAL | METHODOLOGY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | SHRINKAGE | ROBUST UNCERTAINTY PRINCIPLES | Aerospace engineering | Error analysis | Approximation | Partial differential equations | Mathematical analysis | Legacy | Probability theory | Mathematical models | Stochasticity | Sampling | DIFFERENTIAL EQUATIONS | ERRORS | STOCHASTIC PROCESSES | APPROXIMATIONS | CALCULATION METHODS | EQUATIONS | CORRELATIONS | FUNCTIONS | CHAOS THEORY | POLYNOMIALS | MATHEMATICS | MATHEMATICAL SOLUTIONS | PROBABILITY | PARTIAL DIFFERENTIAL EQUATIONS | PROBABILISTIC ESTIMATION | MATHEMATICAL METHODS AND COMPUTING

Uncertainty quantification | Polynomial chaos | Sparse approximation | Compressive sampling | Stochastic PDE | RECONSTRUCTION | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | ATOMIC DECOMPOSITION | PHYSICS, MATHEMATICAL | METHODOLOGY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | SHRINKAGE | ROBUST UNCERTAINTY PRINCIPLES | Aerospace engineering | Error analysis | Approximation | Partial differential equations | Mathematical analysis | Legacy | Probability theory | Mathematical models | Stochasticity | Sampling | DIFFERENTIAL EQUATIONS | ERRORS | STOCHASTIC PROCESSES | APPROXIMATIONS | CALCULATION METHODS | EQUATIONS | CORRELATIONS | FUNCTIONS | CHAOS THEORY | POLYNOMIALS | MATHEMATICS | MATHEMATICAL SOLUTIONS | PROBABILITY | PARTIAL DIFFERENTIAL EQUATIONS | PROBABILISTIC ESTIMATION | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 2/2019, Volume 159, Issue 1, pp. 11 - 27

Fractal interpolation and approximation received a lot of attention in the last thirty years...

65D017 | Computational Mathematics and Numerical Analysis | 30E10 | Fractal Fourier series | 28A80 | Probability Theory and Stochastic Processes | Mathematics | Fractal trigonometric approximation | Bernstein polynomials | Convergence | Fractal approximation | Calculus of Variations and Optimal Control; Optimization | 41A30 | Applications of Mathematics | Partial Differential Equations | 41A17 | Î± $\alpha $ -Fractal functions | Î±-Fractal functions | MATHEMATICS, APPLIED | alpha-Fractal functions | Interpolation | Approximation | Periodic functions | Mathematical analysis | Approximants | Fractals | Polynomials | Trigonometric functions | Fourier series | Continuity (mathematics) | Scaling factors

65D017 | Computational Mathematics and Numerical Analysis | 30E10 | Fractal Fourier series | 28A80 | Probability Theory and Stochastic Processes | Mathematics | Fractal trigonometric approximation | Bernstein polynomials | Convergence | Fractal approximation | Calculus of Variations and Optimal Control; Optimization | 41A30 | Applications of Mathematics | Partial Differential Equations | 41A17 | Î± $\alpha $ -Fractal functions | Î±-Fractal functions | MATHEMATICS, APPLIED | alpha-Fractal functions | Interpolation | Approximation | Periodic functions | Mathematical analysis | Approximants | Fractals | Polynomials | Trigonometric functions | Fourier series | Continuity (mathematics) | Scaling factors

Journal Article

Journal of computational physics, ISSN 0021-9991, 11/2018, Volume 372, pp. 694 - 718

We develop new approximations of the Moriâ€“Zwanzig equation based on operator series expansions of the orthogonal dynamics propagator...

Dimensional reduction | Generalized Langevin equation | Random waves | Stochastic dynamical systems | STATISTICAL-MECHANICS | HARMONIC-OSCILLATOR | COMPUTE | REPRESENTATION | MODEL | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | OPTIMAL PREDICTION | Analysis | Wave propagation

Dimensional reduction | Generalized Langevin equation | Random waves | Stochastic dynamical systems | STATISTICAL-MECHANICS | HARMONIC-OSCILLATOR | COMPUTE | REPRESENTATION | MODEL | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | OPTIMAL PREDICTION | Analysis | Wave propagation

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 10/2015, Volume 63, Issue 20, pp. 5487 - 5497

.... In this paper we propose a tractable multiobject density approximation that can capture statistical dependence between objects...

multi-object tracking | Target tracking | Density measurement | Estimation | Radar tracking | Approximation methods | FISST | PHD | Standards | RFS | Signal to noise ratio | STOCHASTIC GEOMETRY | SLAM | RANDOM FINITE SETS | MULTITARGET TRACKING | PARTICLE FILTER | KNOWLEDGE EXPLOITATION | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Statistics - Other Statistics

multi-object tracking | Target tracking | Density measurement | Estimation | Radar tracking | Approximation methods | FISST | PHD | Standards | RFS | Signal to noise ratio | STOCHASTIC GEOMETRY | SLAM | RANDOM FINITE SETS | MULTITARGET TRACKING | PARTICLE FILTER | KNOWLEDGE EXPLOITATION | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Statistics - Other Statistics

Journal Article

1977, Mathematics in science and engineering, ISBN 0124301401, Volume 129, xvii, 243

Book

Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 10/2014, Volume 111, Issue 41, pp. 14722 - 14727

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network...

Community structure | Datasets | Histograms | Friendship | Approximation | Blogs | Adjacency matrix | Stochastic models | Estimators | Oracles | Community detection | Graph limits | Graphons | Nonparametric statistics | Sparse networks | sparse networks | graphons | MULTIDISCIPLINARY SCIENCES | graph limits | STOCHASTIC BLOCKMODELS | nonparametric statistics | community detection | Approximation theory | Statistical methods | Research | Mathematical research | Physical Sciences

Community structure | Datasets | Histograms | Friendship | Approximation | Blogs | Adjacency matrix | Stochastic models | Estimators | Oracles | Community detection | Graph limits | Graphons | Nonparametric statistics | Sparse networks | sparse networks | graphons | MULTIDISCIPLINARY SCIENCES | graph limits | STOCHASTIC BLOCKMODELS | nonparametric statistics | community detection | Approximation theory | Statistical methods | Research | Mathematical research | Physical Sciences

Journal Article

2012, Cambridge tracts in mathematics, ISBN 9781107017771, Volume 192, xiv, 239

... of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space...

Malliavin calculus | Approximation theory | Probability | Mathematics

Malliavin calculus | Approximation theory | Probability | Mathematics

Book

Operations Research, ISSN 0030-364X, 8/2016, Volume 64, Issue 4, pp. 886 - 905

... a simultaneous approximation for all random utility based discrete choice models including the multinomial logit (MNL...

model selection | assortment optimization | choice modeling | Assortment optimization | Model selection | Choice modeling | PRODUCT VARIETY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REVENUE MANAGEMENT | MANAGEMENT | DEMAND SUBSTITUTION | BEHAVIOR | Markov processes | Learning models (Stochastic processes) | Mathematical optimization | Analysis

model selection | assortment optimization | choice modeling | Assortment optimization | Model selection | Choice modeling | PRODUCT VARIETY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REVENUE MANAGEMENT | MANAGEMENT | DEMAND SUBSTITUTION | BEHAVIOR | Markov processes | Learning models (Stochastic processes) | Mathematical optimization | Analysis

Journal Article

Nature Communications, ISSN 2041-1723, 12/2018, Volume 9, Issue 1, pp. 3305 - 15

.... Here we present the linear-mapping approximation that maps systems with protein-promoter interactions onto approximately equivalent systems with no binding reactions...

CELLS | CHEMICAL MASTER EQUATION | KINETICS | QUANTIFICATION | FLUCTUATIONS | MULTIDISCIPLINARY SCIENCES | PROTEIN EXPRESSION | NOISE APPROXIMATION | SIMULATION | Promoter Regions, Genetic | Protein Biosynthesis | Algorithms | Stochastic Processes | Time Factors | Feedback | Proteolysis | RNA, Messenger - genetics | Probability | Transcription, Genetic | Gene Regulatory Networks | RNA, Messenger - metabolism | Binding | Approximation | Computer simulation | Variations | Bifurcations | Switching theory | Mapping | Parameter sensitivity | Gene expression | Peptide mapping | Proteins | Time dependence | Maps | Stochasticity | Gene mapping | Deoxyribonucleic acid--DNA

CELLS | CHEMICAL MASTER EQUATION | KINETICS | QUANTIFICATION | FLUCTUATIONS | MULTIDISCIPLINARY SCIENCES | PROTEIN EXPRESSION | NOISE APPROXIMATION | SIMULATION | Promoter Regions, Genetic | Protein Biosynthesis | Algorithms | Stochastic Processes | Time Factors | Feedback | Proteolysis | RNA, Messenger - genetics | Probability | Transcription, Genetic | Gene Regulatory Networks | RNA, Messenger - metabolism | Binding | Approximation | Computer simulation | Variations | Bifurcations | Switching theory | Mapping | Parameter sensitivity | Gene expression | Peptide mapping | Proteins | Time dependence | Maps | Stochasticity | Gene mapping | Deoxyribonucleic acid--DNA

Journal Article