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Malliavin calculus and densities for singular stochastic partial differential equations
We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove...
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Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus
This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential...
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Malliavin Calculus
Malliavin derivative, integration by parts, closure, chain rule, divergence operator, chaos representations, norms and domains, conditioning and...
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The Malliavin–Stein Method
The Stein’s method, initiated in the 1970s by Charles Stein, is a procedure to estimate the rate of convergence in CLT-like theorems. It gained a new...
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Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus
We study the locally risk minimizing approach in a market driven by jump-diffusion stochastic volatility models. We show that the Malliavin calculus,...
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Selected Topics in Malliavin Calculus Chaos, Divergence and So Much More
This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. It does not contain all...
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The hyperbolic Anderson model: moment estimates of the Malliavin derivatives and applications
In this article, we study the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension
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Space-Time Stochastic Calculus and White Noise
In the first part of this paper I give the historical background to my initial interest in stochastic analysis and to the writing of my book...
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Berry–Esseen–Stein–Malliavin Theory for Fractional Ornstein–Uhlenbeck Process
Using Malliavin calculus along with Stein’s equation, the chapter shows that the distribution of the normalized minimum contrast estimator of the...
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The Total Variation Distance Between the Solutions to Stochastic Volterra Equations and SDEs with Its Applications
In this paper, we study the distance between the solution of stochastic Volterra integral equations and that of ordinary stochastic differential...
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Rate of Convergence in the Smoluchowski-Kramers Approximation for Mean-field Stochastic Differential Equations
In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a...
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Stochastic Calculus via Regularizations
The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the...
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Restoration of Well-Posedness of Infinite-Dimensional Singular ODE’s via Noise
In this paper we aim at generalizing the results of A. K. Zvonkin ( That removes the drift , 22 , 129,
41 ) and A. Y. Veretennikov ( Theory Probab. Appl. , 24... -
The Brownian transport map
Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual...
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Hypoellipticity and Parabolic Hypoellipticity of Nonlocal Operators under Hörmander’s Condition
In this paper, we prove the hypoellipticity and parabolic hypoellipticity of nonlocal operators under Hörmander’s condition. One key step in the...
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Monte Carlo Methods for Pricing American Options
American options are widespread in the financial market. We review various popular techniques used to value American options, as well as Malliavin...
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Approximation to Stochastic Variance Reduced Gradient Langevin Dynamics by Stochastic Delay Differential Equations
We study in this paper weak approximations in Wasserstein-1 distance to stochastic variance reduced gradient Langevin dynamics by stochastic delay...
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Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions
We present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic...