Numerische Mathematik, ISSN 0029-599X, 10/2019, Volume 143, Issue 2, pp. 379 - 421

Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated...

Mathematical Methods in Physics | 65C40 | 65P10 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 70H45 | MATHEMATICS, APPLIED | LANGEVIN DYNAMICS | INTEGRATION

Mathematical Methods in Physics | 65C40 | 65P10 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 70H45 | MATHEMATICS, APPLIED | LANGEVIN DYNAMICS | INTEGRATION

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 1, pp. 778 - 791

In this paper, we prove a threshold result on the existence of a circularly invariant uniformizable probability measure (CIUPM) for linear transformations with...

Circularly invariant uniformizable probability measure (CIUPM) | Uniformly distributed (modulo one) sequence | Linear transformation | Diameter | Existence | Uniqueness

Circularly invariant uniformizable probability measure (CIUPM) | Uniformly distributed (modulo one) sequence | Linear transformation | Diameter | Existence | Uniqueness

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 11/2017, Volume 455, Issue 1, pp. 778 - 791

In this paper, we prove a threshold result on the existence of a circularly invariant uniformizable probability measure (CIUPM) for linear transformations with...

INTERVAL | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | DENSITIES | Linear transformation | Uniqueness | Circularly invariant uniformizable probability measure (CIUPM) | PIECEWISE MONOTONIC TRANSFORMATIONS | Uniformly distributed (modulo one) sequence | Diameter | Existence

INTERVAL | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | DENSITIES | Linear transformation | Uniqueness | Circularly invariant uniformizable probability measure (CIUPM) | PIECEWISE MONOTONIC TRANSFORMATIONS | Uniformly distributed (modulo one) sequence | Diameter | Existence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 655 - 688

Under integrability conditions of the coefficients, the existence, uniqueness and regularity estimates are derived for the invariant probability measure of...

Singular drift | Invariant probability measure | Regime-switching diffusions | Integrability conditions | Weakly coupled elliptic system | MATHEMATICS | MATHEMATICS, APPLIED | RECURRENCE | STRONG FELLER

Singular drift | Invariant probability measure | Regime-switching diffusions | Integrability conditions | Weakly coupled elliptic system | MATHEMATICS | MATHEMATICS, APPLIED | RECURRENCE | STRONG FELLER

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 195 - 211

We extend Ando–Hiai's log-majorization for the weighted geometric mean of positive definite matrices into that for the Cartan barycenter in the general setting...

Lie–Trotter formula | Wasserstein distance | Log-majorization | Unitarily invariant norm | Cartan barycenter | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Trotter formula | INEQUALITIES | MATRICES

Lie–Trotter formula | Wasserstein distance | Log-majorization | Unitarily invariant norm | Cartan barycenter | Positive definite matrix | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Trotter formula | INEQUALITIES | MATRICES

Journal Article

6.
Full Text
Invariant Borel probability measures for discrete long-wave-short-wave resonance equations

Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 339, pp. 853 - 865

In this article we study the Borel probability measures that can be associated to the time averaged observation of the process generated by the non-autonomous...

Long-wave-short-wave resonance equations | Invariant measures | Lattice dynamical system | Pullback attractor | MATHEMATICS, APPLIED | BEHAVIOR | NOISE | LATTICE DYNAMICAL-SYSTEMS | NONAUTONOMOUS 2D-NAVIER-STOKES EQUATIONS | PULLBACK ATTRACTORS | INFINITE LATTICES | DISPERSIVE WAVES | UNBOUNDED-DOMAINS | COMPACT KERNEL SECTIONS | Information science

Long-wave-short-wave resonance equations | Invariant measures | Lattice dynamical system | Pullback attractor | MATHEMATICS, APPLIED | BEHAVIOR | NOISE | LATTICE DYNAMICAL-SYSTEMS | NONAUTONOMOUS 2D-NAVIER-STOKES EQUATIONS | PULLBACK ATTRACTORS | INFINITE LATTICES | DISPERSIVE WAVES | UNBOUNDED-DOMAINS | COMPACT KERNEL SECTIONS | Information science

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 02/2015, Volume 422, Issue 1, pp. 478 - 495

We characterize rearrangement invariant spaces X with respect to a suitable 1-dimensional probability mu (e.g log-concave measure) such that the Sobolev...

MATHEMATICS | MATHEMATICS, APPLIED | Rearrangement invariant space | INEQUALITIES | BMO space | Weak-L-infinity space | SPACES | 1-dimensional log-concave probability measure | Embedding | H-1

MATHEMATICS | MATHEMATICS, APPLIED | Rearrangement invariant space | INEQUALITIES | BMO space | Weak-L-infinity space | SPACES | 1-dimensional log-concave probability measure | Embedding | H-1

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2015, Volume 422, Issue 1, pp. 478 - 495

We characterize rearrangement invariant spaces with respect to a suitable 1-dimensional probability ( log-concave measure) such that the Sobolev embedding...

1-dimensional log-concave probability measure | Embedding | Weak-[formula omitted] space | Rearrangement invariant space | BMO space | Weak-L | space | Iron oxides

1-dimensional log-concave probability measure | Embedding | Weak-[formula omitted] space | Rearrangement invariant space | BMO space | Weak-L | space | Iron oxides

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 12/2018, Volume 172, Issue 3, pp. 1181 - 1214

In terms of a nice reference probability measure, integrability conditions on the path-dependent drift are presented for (infinite-dimensional) degenerate PDEs...

60J75 | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Sobolev space | 60G52 | Theoretical, Mathematical and Computational Physics | Functional SDEs | Probability Theory and Stochastic Processes | Invariant probability measure | Mathematics | Quantitative Finance | Density | 47G20 | Operations Research/Decision Theory | Integrability condition | FUNCTIONAL INEQUALITIES | THEOREM | SPACES | STRONG UNIQUENESS | EQUATIONS | STATISTICS & PROBABILITY | GRADIENT | HEAT | SDES | HARNACK INEQUALITY | Differential equations | Partial differential equations | Uniqueness | Drift | Entropy | Integral calculus | Estimates | Invariants

60J75 | Statistics for Business, Management, Economics, Finance, Insurance | Mathematical and Computational Biology | Sobolev space | 60G52 | Theoretical, Mathematical and Computational Physics | Functional SDEs | Probability Theory and Stochastic Processes | Invariant probability measure | Mathematics | Quantitative Finance | Density | 47G20 | Operations Research/Decision Theory | Integrability condition | FUNCTIONAL INEQUALITIES | THEOREM | SPACES | STRONG UNIQUENESS | EQUATIONS | STATISTICS & PROBABILITY | GRADIENT | HEAT | SDES | HARNACK INEQUALITY | Differential equations | Partial differential equations | Uniqueness | Drift | Entropy | Integral calculus | Estimates | Invariants

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 12/2014, Volume 157, Issue 6, pp. 1097 - 1113

We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the...

Non-wandering set | Physical Chemistry | Invariant measure | Theoretical, Mathematical and Computational Physics | Quantum Physics | 37A05 | Statistical Physics, Dynamical Systems and Complexity | Physics | Impulsive dynamical system | SEMIDYNAMICAL SYSTEMS | EQUATIONS | DYNAMICS | FLOWS | MODEL | PHYSICS, MATHEMATICAL | PULSE VACCINATION | Mathematics - Dynamical Systems

Non-wandering set | Physical Chemistry | Invariant measure | Theoretical, Mathematical and Computational Physics | Quantum Physics | 37A05 | Statistical Physics, Dynamical Systems and Complexity | Physics | Impulsive dynamical system | SEMIDYNAMICAL SYSTEMS | EQUATIONS | DYNAMICS | FLOWS | MODEL | PHYSICS, MATHEMATICAL | PULSE VACCINATION | Mathematics - Dynamical Systems

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 02/2018, Volume 22, Issue 1, pp. 79 - 94

We study the probability measures on the open convex cone of positive definite operators equipped with the Loewner ordering. We show that two crucial push...

Loewner order | Karcher barycenter | Wasserstein distance | Unitarily invariant norm | Max-flow and min-cut theorem | Stochastic order | MATHEMATICS | POSITIVE-DEFINITE MATRICES

Loewner order | Karcher barycenter | Wasserstein distance | Unitarily invariant norm | Max-flow and min-cut theorem | Stochastic order | MATHEMATICS | POSITIVE-DEFINITE MATRICES

Journal Article

12.
Full Text
Invariant relative probability measures for discrete dynamical systems created by maps

Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 04/2019, Volume 22, Issue 3, pp. 387 - 404

In this paper we consider the maps which preserve a relative probability measure on a set M. We prove that a mapping g : M → M preserves a relative probability...

Invariant relative probability measure | Ergodic | Relative probability measure | Observer | Fixed point

Invariant relative probability measure | Ergodic | Relative probability measure | Observer | Fixed point

Journal Article

Lecture Notes in Mathematics, ISSN 0075-8434, 2018, Volume 2217, pp. 77 - 83

Let (R, sigma) be a transfer operator defined on the space of Borel functions.F(X, B). The main theme of this chapter is the study of a dual action of R on the...

Normalized transfer operator | Probability measures | R-invariant measures | MATHEMATICS

Normalized transfer operator | Probability measures | R-invariant measures | MATHEMATICS

Journal Article

Infinite Dimensional Analysis, Quantum Probability and Related Topics, ISSN 0219-0257, 12/2017, Volume 20, Issue 4

By using the integration by parts formula of a Markov operator, the closability of quadratic forms associated to the corresponding invariant probability...

integration by parts formula | invariant probability measure | Closability | semi-linear SPDEs | MATHEMATICS, APPLIED | EQUATIONS | SYSTEMS | STATISTICS & PROBABILITY | HARNACK INEQUALITY | PHYSICS, MATHEMATICAL | MILD SOLUTIONS

integration by parts formula | invariant probability measure | Closability | semi-linear SPDEs | MATHEMATICS, APPLIED | EQUATIONS | SYSTEMS | STATISTICS & PROBABILITY | HARNACK INEQUALITY | PHYSICS, MATHEMATICAL | MILD SOLUTIONS

Journal Article

Malaysian Journal of Mathematical Sciences, ISSN 1823-8343, 2016, Volume 10, pp. 347 - 359

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2015, Volume 35, Issue 7, pp. 2905 - 2920

We use Wasserstein metrics adapted to study the action of the flow of the BBM equation on probability measures. We prove the continuity of this flow and the...

Stability | Global estimates | Benjamin-Bona-Mahony equation | Invariant measures | Wasserstein metrics | MATHEMATICS | invariant measures | STATISTICAL-MECHANICS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | SYSTEMS | NONLINEAR SCHRODINGER-EQUATION | BBM | stability | global estimates

Stability | Global estimates | Benjamin-Bona-Mahony equation | Invariant measures | Wasserstein metrics | MATHEMATICS | invariant measures | STATISTICAL-MECHANICS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | SYSTEMS | NONLINEAR SCHRODINGER-EQUATION | BBM | stability | global estimates

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 254, Issue 10, pp. 2690 - 2705

We consider the set of all probability measures on satisfying an elliptic equation in the weak worm. We give sufficient conditions in order that this set...

Nonuniqueness | Elliptic equation for measures | MATHEMATICS | INVARIANT-MEASURES | nonuniqueness | TRANSITION-PROBABILITIES | REGULARITY | SINGULAR DIFFUSIONS | elliptic equation for measures | UNIQUENESS

Nonuniqueness | Elliptic equation for measures | MATHEMATICS | INVARIANT-MEASURES | nonuniqueness | TRANSITION-PROBABILITIES | REGULARITY | SINGULAR DIFFUSIONS | elliptic equation for measures | UNIQUENESS

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 1/2008, Volume 130, Issue 2, pp. 343 - 371

In 1993, Majda proposed a simple, random shear model from which scalar intermittency was rigorously predicted for the invariant probability measure of passive...

Physical Chemistry | Mathematical and Computational Physics | Quantum Physics | Scalar intermittency | Turbulent transport | Invariant measures | Physics | Statistical Physics | INTERMITTENCY | turbulent transport | DISSIPATION | TURBULENT-DIFFUSION | PHYSICS, MATHEMATICAL | PASSIVE SCALAR | EXPONENTIAL TAILS | EXPLICIT EXAMPLE | DISTRIBUTIONS | invariant measures | TEMPERATURE | scalar intermittency | VELOCITY-FIELD | RAYLEIGH-BENARD CONVECTION

Physical Chemistry | Mathematical and Computational Physics | Quantum Physics | Scalar intermittency | Turbulent transport | Invariant measures | Physics | Statistical Physics | INTERMITTENCY | turbulent transport | DISSIPATION | TURBULENT-DIFFUSION | PHYSICS, MATHEMATICAL | PASSIVE SCALAR | EXPONENTIAL TAILS | EXPLICIT EXAMPLE | DISTRIBUTIONS | invariant measures | TEMPERATURE | scalar intermittency | VELOCITY-FIELD | RAYLEIGH-BENARD CONVECTION

Journal Article

2003, Lecture notes in mathematics, ISBN 9783540002352, Volume 1808, 177

Symmetries and invariance principles play an important role in various branches of mathematics. This book deals with measures having weak symmetry properties....

Measure theory | Probability measures | Set functions | Numerical analysis | Topological Groups, Lie Groups | Mathematical statistics | Statistical Theory and Methods | Mathematics | Topological Groups | Measure and Integration

Measure theory | Probability measures | Set functions | Numerical analysis | Topological Groups, Lie Groups | Mathematical statistics | Statistical Theory and Methods | Mathematics | Topological Groups | Measure and Integration

eBook

Automatica, ISSN 0005-1098, 09/2014, Volume 50, Issue 9, pp. 2397 - 2404

This paper addresses the problem of control synthesis for locally stabilizing and minimizing the finite ℓ gain for discrete-time Markov jump Lur'e systems with...

Markov chain | Lur'e-type Lyapunov function | Bounded sector nonlinearity | Saturation | Invariant probability measure

Markov chain | Lur'e-type Lyapunov function | Bounded sector nonlinearity | Saturation | Invariant probability measure

Journal Article

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