Stochastic Processes and their Applications, ISSN 0304-4149, 08/2018, Volume 128, Issue 8, pp. 2489 - 2537

Suppose B is a Brownian motion and Bn is an approximating sequence of rescaled random walks on the same probability space converging to B pointwise in...

Strong approximation | Stochastic integrals | Invariance principle | Malliavin calculus | Chaos decomposition | S-transform | STOCHASTIC DIFFERENTIAL-EQUATIONS | ROBUSTNESS | SEQUENCES | BSDES | STATISTICS & PROBABILITY | INTEGRALS | CHAOS | LIMIT-THEOREMS | CONVERGENCE | FUNCTIONALS

Strong approximation | Stochastic integrals | Invariance principle | Malliavin calculus | Chaos decomposition | S-transform | STOCHASTIC DIFFERENTIAL-EQUATIONS | ROBUSTNESS | SEQUENCES | BSDES | STATISTICS & PROBABILITY | INTEGRALS | CHAOS | LIMIT-THEOREMS | CONVERGENCE | FUNCTIONALS

Journal Article

The Annals of probability, ISSN 0091-1798, 2013, Volume 41, Issue 1, pp. 109 - 133

We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Itô...

Differential calculus | Mathematical theorems | Approximation | Integrands | Mathematical integrals | Directional derivatives | Calculus | Martingales | Mathematical integration | functional calculus | functional Ito formula | Malliavin derivative | Wiener functionals | Stochastic calculus | semimartingale | Clark-Ocone formula | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | martingale representation | FORMULA | MALLIAVIN CALCULUS | Functional Analysis | Probability | Mathematics | 60G44 | Clark–Ocone formula | 60H07 | 60H05 | 60H25 | functional Itô formula

Differential calculus | Mathematical theorems | Approximation | Integrands | Mathematical integrals | Directional derivatives | Calculus | Martingales | Mathematical integration | functional calculus | functional Ito formula | Malliavin derivative | Wiener functionals | Stochastic calculus | semimartingale | Clark-Ocone formula | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | martingale representation | FORMULA | MALLIAVIN CALCULUS | Functional Analysis | Probability | Mathematics | 60G44 | Clark–Ocone formula | 60H07 | 60H05 | 60H25 | functional Itô formula

Journal Article

2016, 2nd edition., De Gruyter studies in mathematics, ISBN 3110378086, Volume 54, x, 278

Book

Stochastic processes and their applications, ISSN 0304-4149, 2010, Volume 120, Issue 5, pp. 622 - 652

We trace Itô’s early work in the 1940s, concerning stochastic integrals, stochastic differential equations (SDEs) and Itô’s formula. Then we study its...

Itô’s formula | Black–Scholes equation | Merton’s equation | Jump–diffusion | Stochastic differential equation | Black-Scholes equation | Itô's formula | Merton's equation | Jump-diffusion | STATISTICS & PROBABILITY | Ito's formula | MALLIAVIN CALCULUS | Ito's formula Stochastic differential equation Jump-diffusion Black-Scholes equation Merton's equation

Itô’s formula | Black–Scholes equation | Merton’s equation | Jump–diffusion | Stochastic differential equation | Black-Scholes equation | Itô's formula | Merton's equation | Jump-diffusion | STATISTICS & PROBABILITY | Ito's formula | MALLIAVIN CALCULUS | Ito's formula Stochastic differential equation Jump-diffusion Black-Scholes equation Merton's equation

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 04/2020, Volume 130, Issue 4, pp. 2384 - 2406

In this paper, we use Malliavin calculus to show the existence and continuity of density functions of d-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson...

Non-degeneracy | Dyson Brownian motion | Malliavin calculus | Hyperbolic particle system | Non-colliding particle system | BROWNIAN-MOTION | DENSITIES | SMOOTHNESS | STATISTICS & PROBABILITY

Non-degeneracy | Dyson Brownian motion | Malliavin calculus | Hyperbolic particle system | Non-colliding particle system | BROWNIAN-MOTION | DENSITIES | SMOOTHNESS | STATISTICS & PROBABILITY

Journal Article

2010, Mathematical surveys and monographs, ISBN 9780821849934, Volume 164, xv, 488

Book

Journal of Functional Analysis, ISSN 0022-1236, 01/2017, Volume 272, Issue 2, pp. 421 - 497

For stochastic conservation laws driven by a semilinear noise term, we propose a generalization of the Kružkov entropy condition by allowing the Kružkov...

Stochastic conservation law | Malliavin calculus | Existence | Uniqueness | MATHEMATICS | TRANSPORT-EQUATIONS | Environmental law

Stochastic conservation law | Malliavin calculus | Existence | Uniqueness | MATHEMATICS | TRANSPORT-EQUATIONS | Environmental law

Journal Article

1987, Pitman monographs and surveys in pure and applied mathematics, ISBN 9780470207499, Volume 34, x, 105

Book

Journal of Differential Equations, ISSN 0022-0396, 10/2018, Volume 265, Issue 7, pp. 3168 - 3211

...–time noise of unbounded diffusion. We apply Malliavin calculus, in order to investigate the existence of a density for the stochastic solution u...

Stochastic partial differential equations | Reaction–diffusion equations | Malliavin calculus | Phase transitions | SHARP INTERFACE LIMIT | EXISTENCE | MATHEMATICS | MOTION | Reaction-diffusion equations

Stochastic partial differential equations | Reaction–diffusion equations | Malliavin calculus | Phase transitions | SHARP INTERFACE LIMIT | EXISTENCE | MATHEMATICS | MOTION | Reaction-diffusion equations

Journal Article

01/2005, ISBN 9780849340307

Book

Infinite Dimensional Analysis, Quantum Probability and Related Topics, ISSN 0219-0257, 09/2018, Volume 21, Issue 3

The classical maximum principle for optimal stochastic control states that if a control it is optimal, then the corresponding Hamiltonian has a maximum at u =...

backward stochastic differential equation (BSDE) | Hida-Malliavin calculus | white noise theory | Stochastic maximum principle | spike perturbation | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | PHYSICS, MATHEMATICAL | Hida Malliavin calculus

backward stochastic differential equation (BSDE) | Hida-Malliavin calculus | white noise theory | Stochastic maximum principle | spike perturbation | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | PHYSICS, MATHEMATICAL | Hida Malliavin calculus

Journal Article

The Annals of Statistics, ISSN 0090-5364, 6/2007, Volume 35, Issue 3, pp. 1183 - 1212

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for...

Brownian motion | Integers | Maximum likelihood estimation | Stochastic processes | Differential equations | Inference for Stochastic Processes | Maximum likelihood estimators | Calculus | Random variables | Estimators | Consistent estimators | Maximum | Strong consistency | Hurst parameter | Likelihood estimator | Malliavin calculus | Fractional Brownian motion | Stochastic differential equation | maximum likelihood estimator | MAXIMUM-LIKELIHOOD-ESTIMATION | MODELS | stochastic differential equation | strong consistency | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | fractional Brownian motion | INFERENCE | Probability | Statistics | Mathematics | Maximum likelihood estimator | 60H10 | 62M09 | 60H07 | 60G18

Brownian motion | Integers | Maximum likelihood estimation | Stochastic processes | Differential equations | Inference for Stochastic Processes | Maximum likelihood estimators | Calculus | Random variables | Estimators | Consistent estimators | Maximum | Strong consistency | Hurst parameter | Likelihood estimator | Malliavin calculus | Fractional Brownian motion | Stochastic differential equation | maximum likelihood estimator | MAXIMUM-LIKELIHOOD-ESTIMATION | MODELS | stochastic differential equation | strong consistency | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | fractional Brownian motion | INFERENCE | Probability | Statistics | Mathematics | Maximum likelihood estimator | 60H10 | 62M09 | 60H07 | 60G18

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2015, Volume 167, Issue 3, pp. 1070 - 1094

.... However, we show that using Malliavin calculus, it is possible to formulate modified functional types of maximum principle suitable for such systems...

60H20 | Primary 60H07 | Maximum principle | Mathematics | Theory of Computation | Optimization | Partial information | 93E20 | Calculus of Variations and Optimal Control; Optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Stochastic Volterra equations | Malliavin calculus | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTEGRAL-EQUATIONS | Markov processes | Investment analysis | Financial markets | Analysis | Studies | Stochastic models | Dynamic programming | Integral equations | Mathematical analysis | Optimal control | Mathematical models | Calculus | Stochasticity | Dynamical systems

60H20 | Primary 60H07 | Maximum principle | Mathematics | Theory of Computation | Optimization | Partial information | 93E20 | Calculus of Variations and Optimal Control; Optimization | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Stochastic Volterra equations | Malliavin calculus | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTEGRAL-EQUATIONS | Markov processes | Investment analysis | Financial markets | Analysis | Studies | Stochastic models | Dynamic programming | Integral equations | Mathematical analysis | Optimal control | Mathematical models | Calculus | Stochasticity | Dynamical systems

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2017, Volume 272, Issue 1, pp. 363 - 419

Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension...

Generalized parabolic Anderson model | Regularity structures | Malliavin calculus | Singular SPDEs | MATHEMATICS | THEOREM | PATHS | ROUGH DIFFERENTIAL-EQUATIONS | DRIVEN | Probability | Mathematics

Generalized parabolic Anderson model | Regularity structures | Malliavin calculus | Singular SPDEs | MATHEMATICS | THEOREM | PATHS | ROUGH DIFFERENTIAL-EQUATIONS | DRIVEN | Probability | Mathematics

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 03/2012, Volume 122, Issue 3, pp. 808 - 843

The Malliavin derivative, the divergence operator (Skorokhod integral), and the Ornstein–Uhlenbeck operator are extended from the traditional Gaussian setting...

Generalized stochastic processes | Stochastic PDEs | Malliavin operators | WIENER CHAOS | STOCHASTIC-EVOLUTION EQUATIONS | STATISTICS & PROBABILITY | NOISE | DRIVEN

Generalized stochastic processes | Stochastic PDEs | Malliavin operators | WIENER CHAOS | STOCHASTIC-EVOLUTION EQUATIONS | STATISTICS & PROBABILITY | NOISE | DRIVEN

Journal Article

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

.... Probab. 33 (2005) 177–193] using techniques of Malliavin calculus. Finally, we extend our result to the multidimensional case and prove a weak convergence result...

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

The Annals of probability, ISSN 0091-1798, 2001, Volume 29, Issue 2, pp. 766 - 801

In this paper we develop a stochastic calculus with respect to a Gaussian process of the form B = ∫ K...

Brownian motion | Mathematical theorems | Covariance | Mathematical integrals | Adjoints | Indefinite integrals | Riemann sums | Random variables | Calculus of variations | Mathematical integration | Itô's formula | Malliavin calculus | Fractional Brownian motion | Stochastic integral | STATISTICS & PROBABILITY | stochastic integral | fractional Brownian motion | FORMULA | Ito's formula | 60H07 | 60N05

Brownian motion | Mathematical theorems | Covariance | Mathematical integrals | Adjoints | Indefinite integrals | Riemann sums | Random variables | Calculus of variations | Mathematical integration | Itô's formula | Malliavin calculus | Fractional Brownian motion | Stochastic integral | STATISTICS & PROBABILITY | stochastic integral | fractional Brownian motion | FORMULA | Ito's formula | 60H07 | 60N05

Journal Article

Journal of Statistical Planning and Inference, ISSN 0378-3758, 07/2020, Volume 207, pp. 155 - 180

...+14 and we estimate the rate of convergence for it via the Stein–Malliavin calculus. The results are applied to the estimation of the Hurst index...

Hurst parameter estimation | Central limit theorem | Stochastic wave equation | Stein–Malliavin calculus | Fractional Brownian motion | Generalized variation | Stein-Malliavin calculus | STATISTICS & PROBABILITY | DRIVEN | INDEX | INFERENCE | ROSENBLATT PROCESS | QUADRATIC VARIATIONS

Hurst parameter estimation | Central limit theorem | Stochastic wave equation | Stein–Malliavin calculus | Fractional Brownian motion | Generalized variation | Stein-Malliavin calculus | STATISTICS & PROBABILITY | DRIVEN | INDEX | INFERENCE | ROSENBLATT PROCESS | QUADRATIC VARIATIONS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2014, Volume 60, Issue 3, pp. 1963 - 1975

.... Using the techniques of the Malliavin calculus, we study the existence of this object and its properties...

scaling | high frequency financial data | Biological system modeling | Noise | Stochastic processes | multifractal random walk | Fractals | Calculus | Brownian motion | leverage effect | Mathematical model | Malliavin calculus | Fractional Brownian motion | infinitely divisible cascades | COMPUTER SCIENCE, INFORMATION SYSTEMS | CASCADES | MODEL | ENGINEERING, ELECTRICAL & ELECTRONIC | FLUCTUATIONS | CONDITIONAL HETEROSKEDASTICITY | ASSET RETURNS | Signal processing | Usage | Numerical analysis | Integral equations | Innovations

scaling | high frequency financial data | Biological system modeling | Noise | Stochastic processes | multifractal random walk | Fractals | Calculus | Brownian motion | leverage effect | Mathematical model | Malliavin calculus | Fractional Brownian motion | infinitely divisible cascades | COMPUTER SCIENCE, INFORMATION SYSTEMS | CASCADES | MODEL | ENGINEERING, ELECTRICAL & ELECTRONIC | FLUCTUATIONS | CONDITIONAL HETEROSKEDASTICITY | ASSET RETURNS | Signal processing | Usage | Numerical analysis | Integral equations | Innovations

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 2007, Volume 117, Issue 11, pp. 1689 - 1723

.... A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is to investigate connections between Malliavin estimators and the more traditional and elementary pathwise method and likelihood ratio method...

Likelihood ratio method | Weak convergence | Pathwise derivative method | Malliavin calculus | Monte Carlo simulation | Monte Carlo simulation Likelihood ratio method Pathwise derivative method Malliavin calculus Weak convergence

Likelihood ratio method | Weak convergence | Pathwise derivative method | Malliavin calculus | Monte Carlo simulation | Monte Carlo simulation Likelihood ratio method Pathwise derivative method Malliavin calculus Weak convergence

Journal Article

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