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Wasserstein Distance Estimates for Stochastic Integrals by Forward-Backward Stochastic Calculus
We prove Wasserstein distance bounds between the probability distributions of stochastic integrals with jumps, based on the integrands appearing in...
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Central limit theorems for nonlinear stochastic wave equations in dimension three
In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some...
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Applications of Lévy Differential Operators in the Theory of Gauge Fields
This paper is a survey of results on the relationship between gauge fields and infinitedimensional equations for parallel transport that contain the...
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Integration by Parts Formula for Exit Times of One Dimensional Diffusions
In line with the methodology introduced in Frikha et al. (Electron J Probab 24(95):1–44, 2019) for formulating probabilistic representations of...
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The Future of Probability
Probability as a subject in and of itself has rarely been truly appreciated by mathematicians in other disciplines. This has gradually changed over...
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Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise
We prove absolute continuity of the law of the solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L 2 (
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Bismut’s Way of the Malliavin Calculus for Non-Markovian Semi-groups: An Introduction
We give a review of our recent works related to the Malliavin calculus of Bismut type for non-Markovian generators. Part IV is new and relates the...
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Berry–Esseen Asymptotics for Pearson Diffusions
Using Malliavin calculus along with Stein’s equation, the chapter shows that the distribution of the maximum likelihood estimator of the drift...
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Gradient and Divergence
If we put a measure on a Banach space, functions defined on it become random variables and are thus defined up to a negligeable set. This ruins the...
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The Law of the Iterated Logarithm for Spatial Averages of the Stochastic Heat Equation
Let u ( t , x ) be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u (0, x ) = 1 for all x ∈...
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Transfer operators and conditional expectations: the non-commutative case, the case of mu-Brownian motions and white noise space setting
Our focus is the operators of multivariable stochastic calculus, i.e., systems of transfer operators, covariance operators, conditional expectations,...
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Normal Approximation of Kabanov–Skorohod Integrals on Poisson Spaces
We consider the normal approximation of Kabanov–Skorohod integrals on a general Poisson space. Our bounds are for the Wasserstein and the Kolmogorov...
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On the Wiener chaos expansion of the signature of a Gaussian process
We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with...
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A Stochastic Interpretation of the Parametrix Method
We revisit, in a didactic manner and by using stochastic analysis, the parametrix method and its application to unbiased simulation. We consider, in...
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Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two
We study the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two. The equation is driven by a Gaussian...
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Lévy Laplacians in Hida Calculus and Malliavin Calculus
Some connections between different definitions of Lévy Laplacians in the stochastic analysis are considered. Two approaches are used to define these...
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The Convergence Rate from Discrete to Continuous Optimal Investment Stop** Problem
The author studies the optimal investment stop** problem in both continuous and discrete cases, where the investor needs to choose the optimal...