2011, Mathematical surveys and monographs, ISBN 9780821868713, Volume 176, viii, 264

Book

2011, CBMS-NSF regional conference series in applied mathematics, ISBN 9781611972009, Volume 83, xiv, 220

Book

1992, Applications of mathematics, ISBN 3540540628, Volume 23, xxxv, 632

Book

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2006, Volume 463, Issue 2077, pp. 163 - 181

...doi: 10.1098/rspa.2006.1753 , 163-181463 2007 Proc. R. Soc. A Peter E Kloeden and José A Langa attractors Flattening, squeezing and the existence of random...

Sufficient conditions | Determinism | Navier Stokes equation | Differential equations | Trajectories | Mathematics | Random variables | Oblateness | Banach space | Dynamical systems | Squeezing property | Random attractors | Flattening | Random dynamical systems | flattening | MULTIDISCIPLINARY SCIENCES | random dynamical systems | GLOBAL ATTRACTORS | EQUATIONS | squeezing property | RANDOM DYNAMICAL-SYSTEMS | random attractors

Sufficient conditions | Determinism | Navier Stokes equation | Differential equations | Trajectories | Mathematics | Random variables | Oblateness | Banach space | Dynamical systems | Squeezing property | Random attractors | Flattening | Random dynamical systems | flattening | MULTIDISCIPLINARY SCIENCES | random dynamical systems | GLOBAL ATTRACTORS | EQUATIONS | squeezing property | RANDOM DYNAMICAL-SYSTEMS | random attractors

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, ISSN 1364-5021, 02/2009, Volume 465, Issue 2102, pp. 649 - 667

...doi: 10.1098/rspa.2008.0325 , 649-667465 2009 Proc. R. Soc. A Arnulf Jentzen and Peter E Kloeden time noise−equations with additive space approximation...

Approximation | Partial differential equations | Heat equation | Spacetime | Logical givens | Differential equations | White noise | Linear transformations | Numerical schemes | Perceptron convergence procedure | Computational order barrier | Exponential Euler scheme | Galerkin approximation | Parabolic stochastic partial differential equation | exponential Euler scheme | RUNGE-KUTTA METHODS | LATTICE APPROXIMATIONS | parabolic stochastic partial differential equation | MULTIDISCIPLINARY SCIENCES | IMPLICIT SCHEME | computational order barrier | LOCAL LINEARIZATION METHOD | DRIVEN

Approximation | Partial differential equations | Heat equation | Spacetime | Logical givens | Differential equations | White noise | Linear transformations | Numerical schemes | Perceptron convergence procedure | Computational order barrier | Exponential Euler scheme | Galerkin approximation | Parabolic stochastic partial differential equation | exponential Euler scheme | RUNGE-KUTTA METHODS | LATTICE APPROXIMATIONS | parabolic stochastic partial differential equation | MULTIDISCIPLINARY SCIENCES | IMPLICIT SCHEME | computational order barrier | LOCAL LINEARIZATION METHOD | DRIVEN

Journal Article

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2010, Volume 467, Issue 2130, pp. 1563 - 1576

The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and...

Platens | Simulations | Monte Carlo methods | Approximation | Eulers method | Infinity | Differential equations | Mathematics | Coefficients | Diffusion coefficient | MATHEMATICS | applied mathematics | computational mathematics | Research articles | Strong approximation | Strong divergence | Euler scheme | Non-globally Lipschitz continuous | Weak approximation | Weak divergence | weak approximation | strong divergence | APPROXIMATIONS | MULTIDISCIPLINARY SCIENCES | strong approximation | CONVERGENCE | SDES | MARUYAMA SCHEME | weak divergence | non-globally Lipschitz continuous

Platens | Simulations | Monte Carlo methods | Approximation | Eulers method | Infinity | Differential equations | Mathematics | Coefficients | Diffusion coefficient | MATHEMATICS | applied mathematics | computational mathematics | Research articles | Strong approximation | Strong divergence | Euler scheme | Non-globally Lipschitz continuous | Weak approximation | Weak divergence | weak approximation | strong divergence | APPROXIMATIONS | MULTIDISCIPLINARY SCIENCES | strong approximation | CONVERGENCE | SDES | MARUYAMA SCHEME | weak divergence | non-globally Lipschitz continuous

Journal Article

The Annals of applied probability, ISSN 1050-5164, 2012, Volume 22, Issue 4, pp. 1611 - 1641

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly...

Platens | Error rates | Approximation | Eulers method | Roots of functions | Numerical methods | Stochastic processes | Differential equations | Coefficients | Perceptron convergence procedure | Strong approximation | Nonglobally Lipschitz | Tamed Euler scheme | Implicit Euler scheme | Superlinearly growing coefficient | Backward Euler scheme | Euler scheme | Euler-Maruyama | Stochastic differential equation | nonglobally Lipschitz | STOCHASTIC DIFFERENTIAL-EQUATIONS | tamed Euler scheme | BEHAVIOR | strong approximation | UNIFORM APPROXIMATION | STATISTICS & PROBABILITY | IMPLICIT METHODS | superlinearly growing coefficient | SCHEME | stochastic differential equation | implicit Euler scheme | SYSTEMS | 65C30 | Euler–Maruyama

Platens | Error rates | Approximation | Eulers method | Roots of functions | Numerical methods | Stochastic processes | Differential equations | Coefficients | Perceptron convergence procedure | Strong approximation | Nonglobally Lipschitz | Tamed Euler scheme | Implicit Euler scheme | Superlinearly growing coefficient | Backward Euler scheme | Euler scheme | Euler-Maruyama | Stochastic differential equation | nonglobally Lipschitz | STOCHASTIC DIFFERENTIAL-EQUATIONS | tamed Euler scheme | BEHAVIOR | strong approximation | UNIFORM APPROXIMATION | STATISTICS & PROBABILITY | IMPLICIT METHODS | superlinearly growing coefficient | SCHEME | stochastic differential equation | implicit Euler scheme | SYSTEMS | 65C30 | Euler–Maruyama

Journal Article

1994, Universitext., ISBN 3540570748, xiv, 292

Book

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 09/2016, Volume 26, Issue 10, p. 1650174

The existence of a pullback attractor for the nonautonomous p -Laplacian type equations on infinite lattices is established under certain natural dissipative...

forward attracting sets | Lattice dynamical systems | asymptotic autonomous systems | pullback attractor | PRINCIPAL PART | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | GLOBAL ATTRACTOR | PARABOLIC EQUATION

forward attracting sets | Lattice dynamical systems | asymptotic autonomous systems | pullback attractor | PRINCIPAL PART | EXISTENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | GLOBAL ATTRACTOR | PARABOLIC EQUATION

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 10/2016, Volume 6, Issue 3, pp. 453 - 514

...Bull. Math. Sci. (2016) 6:453–514 DOI 10.1007/s13373-016-0090-5 Nonlocal multi-scale trafﬁc ﬂow models: analysis beyond vector spaces Peter E. Kloeden 1...

Radon measures | Balance laws | Euler compactness | Mathematics | 35L45 | 34G25 | 49J53 | Nonlocal traffic flow | Mathematics, general | 35B30 | Mutational analysis | 35R06 | Well-posedness | FIELDS | STOCHASTIC DIFFERENTIAL-EQUATIONS | TRANSPORT-EQUATIONS | METRIC-SPACES | APPROXIMATIONS | CAUCHY-PROBLEM | POPULATIONS | SAMPLE DEPENDENCE | UNIQUENESS | MATHEMATICS

Radon measures | Balance laws | Euler compactness | Mathematics | 35L45 | 34G25 | 49J53 | Nonlocal traffic flow | Mathematics, general | 35B30 | Mutational analysis | 35R06 | Well-posedness | FIELDS | STOCHASTIC DIFFERENTIAL-EQUATIONS | TRANSPORT-EQUATIONS | METRIC-SPACES | APPROXIMATIONS | CAUCHY-PROBLEM | POPULATIONS | SAMPLE DEPENDENCE | UNIQUENESS | MATHEMATICS

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 10/2013, Volume 23, Issue 5, pp. 1913 - 1966

The Euler-Maruyama scheme is known to diverge strongly and numerically weakly when applied to nonlinear stochastic differential equations (SDEs) with...

Error rates | Monte Carlo methods | Eulers method | Approximation | Real numbers | Differential equations | Coefficients | Probabilities | Induction assumption | Perceptron convergence procedure | Nonglobally Lipschitz continuous | Nonlinear stochastic differential equations | Rare events | nonglobally Lipschitz continuous | EXISTENCE | SCHEME | COMPLEXITY | nonlinear stochastic differential equations | UNIFORM APPROXIMATION | SYSTEMS | SDES | STATISTICS & PROBABILITY | STRONG-CONVERGENCE | 60H35

Error rates | Monte Carlo methods | Eulers method | Approximation | Real numbers | Differential equations | Coefficients | Probabilities | Induction assumption | Perceptron convergence procedure | Nonglobally Lipschitz continuous | Nonlinear stochastic differential equations | Rare events | nonglobally Lipschitz continuous | EXISTENCE | SCHEME | COMPLEXITY | nonlinear stochastic differential equations | UNIFORM APPROXIMATION | SYSTEMS | SDES | STATISTICS & PROBABILITY | STRONG-CONVERGENCE | 60H35

Journal Article

2002, Universitext, ISBN 9783540426660, xvi, 310

Book

1992, ISBN 3540540628, Volume 23., xxxv, 632

Book

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 09/2010, Volume 20, Issue 9, pp. 2591 - 2636

This paper aims to an present account of some problems considered in the past years in Dynamical Systems, new research directions and also provide some open...

LiYorke chaos | continua | global attractor | non-autonomous and random pullback attractors | set-valued dynamical system | Topological entropy | Lyapunov exponent | ordinary and partial differential equations | non-autonomous systems | difference equations | CONTINUOUS-MAPS | MULTIDISCIPLINARY SCIENCES | GLOBAL ATTRACTORS | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | UNIFORM ATTRACTORS | ASYMPTOTIC-BEHAVIOR | MULTIVALUED SEMIFLOWS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Li-Yorke chaos | NONLINEAR PARABOLIC EQUATIONS | PULLBACK ATTRACTORS | REACTION-DIFFUSION-EQUATIONS

LiYorke chaos | continua | global attractor | non-autonomous and random pullback attractors | set-valued dynamical system | Topological entropy | Lyapunov exponent | ordinary and partial differential equations | non-autonomous systems | difference equations | CONTINUOUS-MAPS | MULTIDISCIPLINARY SCIENCES | GLOBAL ATTRACTORS | DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | UNIFORM ATTRACTORS | ASYMPTOTIC-BEHAVIOR | MULTIVALUED SEMIFLOWS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Li-Yorke chaos | NONLINEAR PARABOLIC EQUATIONS | PULLBACK ATTRACTORS | REACTION-DIFFUSION-EQUATIONS

Journal Article

1994, ISBN 9810217315, ix, 178

Book

Journal of dynamics and differential equations, ISSN 1572-9222, 2019

Journal Article

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, ISSN 1311-0454, 06/2019, Volume 22, Issue 3, pp. 681 - 698

...RESEARCH PAPER THE ASYMPTOTIC BEHAVIOUR OF FRACTIONAL LATTICE SYSTEMS WITH VARIABLE DELAY Linfang Liu 1, Tomás Caraballo 2, Peter E. Kloeden 3 Abstract...

variable delay | MATHEMATICS | MATHEMATICS, APPLIED | fractional lattice systems | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Leray-Schauder theorem | fractional substantial derivative | global attracting sets | ALGORITHMS | Asymptotic properties | Differential equations

variable delay | MATHEMATICS | MATHEMATICS, APPLIED | fractional lattice systems | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Leray-Schauder theorem | fractional substantial derivative | global attracting sets | ALGORITHMS | Asymptotic properties | Differential equations

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, ISSN 1364-5021, 11/2007, Volume 463, Issue 2087, pp. 2929 - 2944

...doi: 10.1098/rspa.2007.0055 , 2929-2944463 2007 Proc. R. Soc. A Peter E Kloeden and Arnulf Jentzen schemes for random ordinary differential equations Pathwise...

Brownian motion | Determinism | Approximation | Odes | Differential equations | Vector fields | Ordinary differential equations | Scalars | Numerical schemes | Cauchy problem | One-step numerical scheme | Taylor-like expansion | Fractional Brownian motion | Pathwise convergence | Random ordinary differential equations | random ordinary differential equations | MULTIDISCIPLINARY SCIENCES | one-step numerical scheme | pathwise convergence | fractional Brownian motion

Brownian motion | Determinism | Approximation | Odes | Differential equations | Vector fields | Ordinary differential equations | Scalars | Numerical schemes | Cauchy problem | One-step numerical scheme | Taylor-like expansion | Fractional Brownian motion | Pathwise convergence | Random ordinary differential equations | random ordinary differential equations | MULTIDISCIPLINARY SCIENCES | one-step numerical scheme | pathwise convergence | fractional Brownian motion

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 07/2018, Volume 36, Issue 4, pp. 654 - 664

Using a temporally weighted norm, we first establish a result on the global existence and uniqueness of solutions for Caputo fractional stochastic differential...

Fractional stochastic differential equations | Asymptotic behavior, Lyapunov exponents | 26A33, 34A08, 34A12, 34D05 Secondary: 60H10 | Continuous dependence on the initial condition | Existence and uniqueness solutions | Temporally weighted norm | MATHEMATICS, APPLIED | Lyapunov exponents | Asymptotic behavior | STATISTICS & PROBABILITY | Lipschitz condition | Mathematical analysis | Formulas (mathematics) | Differential equations | Mathematics - Classical Analysis and ODEs

Fractional stochastic differential equations | Asymptotic behavior, Lyapunov exponents | 26A33, 34A08, 34A12, 34D05 Secondary: 60H10 | Continuous dependence on the initial condition | Existence and uniqueness solutions | Temporally weighted norm | MATHEMATICS, APPLIED | Lyapunov exponents | Asymptotic behavior | STATISTICS & PROBABILITY | Lipschitz condition | Mathematical analysis | Formulas (mathematics) | Differential equations | Mathematics - Classical Analysis and ODEs

Journal Article

20.
Full Text
Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents

Journal of mathematical analysis and applications, ISSN 0022-247X, 2017, Volume 445, Issue 1, pp. 513 - 531

We study the asymptotic behavior of a non-autonomous multivalued Cauchy problem of the form∂u∂t(t)−div(D(t)|∇u(t)|p(x)−2∇u(t))+|u(t)|p(x)−2u(t)+F(t,u(t))∋0 on...

Time-dependent operator | Multivalued Cauchy problem | Variable exponents | Asymptotically autonomous inclusion | Pullback attractors | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SEMIFLOWS

Time-dependent operator | Multivalued Cauchy problem | Variable exponents | Asymptotically autonomous inclusion | Pullback attractors | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SEMIFLOWS

Journal Article

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