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