The Stein-Dirichlet-Malliavin method by Decreusefond L.

“…We show how this procedure can be enriched by Malliavin calculus leading to a functional approach valid in infinite dimensional spaces.…”
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Second order Poincaré inequalities and CLTs on Wiener space by Nourdin, I, Peccati, G, Reinert, G

“…We prove infinite-dimensional second order Poincar\'e inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Stein's method and Malliavin calculus. We provide two applications: (i) to a new "second order" characterization of CLTs on a fixed Wiener chaos, and (ii) to linear functionals of Gaussian-subordinated fields.…”

Morse inequalities, a probabilistic approach by Popescu, Ionel, 1974-

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Fine properties of fractional Brownian motions on Wiener space by Jiawei, L, Qian, Z

“…We regard fractional Brownian motions as Wiener functionals via the integral representation discovered by Decreusefond and Üstünel, and show non-differentiability, modulus of continuity, law of the iterated logarithm (LIL) and self-avoiding properties of fractional Brownian motion sample paths using Malliavin calculus as well as the tools developed in the previous work by Fukushima, Takeda and etc. for Brownian motion case.…”

Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise by Antoine Tambue, Jean Daniel Mukam

“…In contrast to many results in the current scientific literature, we investigate the more general case where the nonlinearity is allowed to be of Nemytskii-type and the linear operator is not necessarily self-adjoint, which is more challenging and models more realistic phenomena such as convection–reaction–diffusion processes. Using Malliavin calculus, Kolmogorov equations and by splitting the linear operator into a self-adjoint and non self-adjoint parts, we prove the convergence of the finite element approximation and obtain a weak convergence rate that is twice the strong convergence rate.…”
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SHORT TIME FULL ASYMPTOTIC EXPANSION OF HYPOELLIPTIC HEAT KERNEL AT THE CUT LOCUS by YUZURU INAHAMA, SETSUO TANIGUCHI

“…Watanabe’s distributional Malliavin calculus and T. Lyons’ rough path theory.…”
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Quantum omega-semimartingales and stochastic evolutions by Belton, A

“…It is shown that the (non-adapted) quantum stochastic integrals of bounded, <em>omega</em>-adapted processes are themselves bounded and <em>omega</em>-adapted, a fact that may be deduced from the Bismut–Clark–Ocone formula of Malliavin calculus. An algebra analogous to Attal’s class <em>S</em> of regular quantum semimartingales is defined, and product and functional Itoˆ formulae are given. …”

Anticipating random periodic solutions I: SDEs with multiplicative linear noise by Feng, C, Wu, Y, Zhao, H

“…We then solve a localised forward–backward IHRIE in C9R,L^2loc (Ω)) using an argument of truncations, the Malliavin calculus, the relative compactness of Wiener–Sobolev spaces in C([0,T], L^2 (Ω)) and Schauder's fixed point theorem. …”

Stochastic evolution equations for large portfolios of stochastic volatility models by Hambly, B, Kolliopoulos, N

“…This limit evolves as a measure valued process and we show that it will have a density given in terms of a solution to a stochastic partial differential equation of filtering type in the two-dimensional half-space, with a Dirichlet boundary condition. We employ Malliavin calculus to establish the existence of a regular density for the volatility component, and an approximation by models of piecewise constant volatilities combined with a kernel smoothing technique to obtain existence and regularity for the full two-dimensional filtering problem. …”

Stochastic Jacobi fields and vector fields induced by varying area on path spaces by Lyons, T, Qian, Z

“…We prove that the vector field obtained by parallel translating a curve in the initial tangent space via a connection is just the vector field generated by translating the path along a direction in the Cameron-Martin space in the Malliavin calculus sense, and at the same time changing its Lévy area in an appropriate way. …”

Analytical and Computational Analysis of Fractional Stochastic Models Using Iterated Itô Integrals by Adeeb Noor, Mohammed Bazuhair, Mohamed El-Beltagy

“…In the current work, FWHE is generalized and adapted to be consistent with the Malliavin calculus approach. The conditions for existence and uniqueness are outlined in addition to the proof of convergence. …”
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Asymptotic expansions and distribution properties for diffusion processes by She, Qihao

“…For this thesis, we derive new applications and theoretical results for some multidimensional mean-reverting stochastic processes via series expansion. We use Malliavin calculus and moment cumulant formula to specify the conditions on the stochastic process, under which, we are able to obtain some conditional Gaussian identities for Brownian stochastic integrals. …”
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Analysis of stochastic PDEs arising from large portfolios of stochastic volatility models by Kolliopoulos, N

“…Next, we employ Malliavin calculus to establish the existence of a regular density for the volatility component of the SPDE, and an approximation by models of piecewise constant volatilities combined with a kernel smoothing technique to obtain existence and regularity for the full two-dimensional filtering problem. …”

Formal verification meets stochastic analysis by Cosentino, F

“…We introduce a grid-free approach for the computation of Probabilistic Safety Regions using Malliavin Calculus.</p>…”