14 citations · 40 across the 19 of their papers we have counts for
24 papers
Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach
Fabian Harang, Chengcheng Ling, Peter H. C. Pang
We establish the existence of weak solutions to a class of distribution-dependent stochastic differential equations (DDSDEs) with possibly degenerate multiplicative noise and singu…
Universal approximation on non-geometric rough paths and applications to financial derivatives pricing
Fabian A. Harang, Fred Espen Benth, Fride Straum
We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximat…
On the signature of an image
Joscha Diehl, Kurusch Ebrahimi-Fard, Fabian Harang +1
Over the past decade, the importance of the 1D signature which can be seen as a functional defined along a path, has been pivotal in both path-wise stochastic calculus and the anal…
Pathwise regularization by noise for semilinear SPDEs driven by a multiplicative cylindrical Brownian motion
Florian Bechtold, Fabian A. Harang
We prove a regularization by noise phenomenon for semilinear SPDEs driven by multiplicative cylindrical Brownian motion and singular diffusion coefficient. The analysis is based on…
A multiparameter Stochastic Sewing lemma and the regularity of local times associated to Gaussian sheets
Florian Bechtold, Fabian A. Harang, Hannes Kern
We establish a multiparameter extension of the stochastic sewing lemma. This allows us to derive novel regularity estimates on the local time of locally non-deterministic Gaussian…
Dynamic spending and portfolio decisions with a soft social norm
Knut Anton Mork, Fabian Andsem Harang, Haakon Andreas Trønnes +1
We explore the implications of a preference ordering for an investor-consumer with a strong preference for keeping consumption above an exogenous social norm, but who is willing to…
Non-linear Young equations in the plane and pathwise regularization by noise for the stochastic wave equation
Florian Bechtold, Fabian A. Harang, Nimit Rana
We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stochastic Process. Appl., 2016). To this e…
Volterra equations driven by rough signals 3: Probabilistic construction of the Volterra rough path for fractional Brownian motions
Fabian Harang, Samy Tindel, Xiaohua Wang
Based on the recent development of the framework of Volterra rough paths, we consider here the probabilistic construction of the Volterra rough path associated to the fractional Br…
Distribution dependent SDEs driven by additive fractional Brownian motion
Lucio Galeati, Fabian A. Harang, Avi Mayorcas
We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter…
Distribution dependent SDEs driven by additive continuous noise
Lucio Galeati, Fabian A. Harang, Avi Mayorcas
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We…
Volterra equations driven by rough signals 2: higher order expansions
Fabian A. Harang, Samy Tindel, Xiaohua Wang
We extend the recently developed rough path theory for Volterra equations from (Harang and Tindel, 2019) to the case of more rough noise and/or more singular Volterra kernels. It w…
Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation
Rémi Catellier, Fabian A. Harang
Existence and uniqueness of solutions to the stochastic heat equation with multiplicative spatial noise is studied. In the spirit of pathwise regularization by noise, we show that…
Pathwise Regularisation of Singular Interacting Particle Systems and their Mean Field Limits
Fabian Harang, Avi Mayorcas
We investigate the regularizing effect of certain perturbations by noise in singular interacting particle systems under the mean field scaling. In particular, we show that the addi…
Regularization of multiplicative SDEs through additive noise
Lucio Galeati, Fabian A. Harang
We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz require…
Hybrid Template Canonical Correlation Analysis Method for Enhancing SSVEP Recognition under data-limited Condition
Runfeng Miao, Li Zhang, Qiang Sun
In this study, an advanced CCA-based algorithn called hybrid template canonical correlation analysis (HTCCA) was proposed to improve the performance of brain-computer interface (BC…
Regularity of Local times associated to Volterra-Lévy processes and path-wise regularization of stochastic differential equations
Fabian A. Harang, Chengcheng Ling
We investigate the space-time regularity of the local time associated to Volterra-Lévy processes, including Volterra processes driven by -stable processes for . We sh…
Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications
Fred E. Benth, Fabian A. Harang
We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals of deterministic kernels with respect to the Hölder continuous traj…
C-infinity regularization of ODEs perturbed by noise
Fabian A. Harang, Nicolas Perkowski
We study ODEs with vector fields given by general Schwartz distributions, and we show that if we perturb such an equation by adding an "infinitely regularizing" path, then it has a…
Volterra Equations Driven by Rough Signals
Fabian A. Harang, Samy Tindel
This article is devoted to the extension of the theory of rough paths in the context of Volterra equations with possibly singular kernels. We begin to describe a class of two param…
Self-Exciting Multifractional Processes
Fabian A. Harang, Marc Lagunas-Merino, Salvador Ortiz-Latorre
We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenom…
An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi parameter Young fields
Fabian A. Harang
This article extends the celebrated sewing lemma to multi-parameter fields on hyper cubes. We use this to construct Young integrals for multi-parameter Hölder fields on general dom…
A Bismut-Elworthy-Li Formula for Singular SDE's Driven by a Fractional Brownian Motion and Applications to Rough Volatility Modeling
Oussama Amine, Emmanuel Coffie, Fabian Harang +1
In this paper we derive a Bismut-Elworthy-Li type formula with respect to strong solutions to singular stochastic differential equations (SDE's) with additive noise given by a mult…
Differential Equations Driven by Variable Order Hölder Noise, and the Regularizing Effect of Delay
Fabian A. Harang
In this article we extend the framework of rough paths to processes of variable Hölder exponent or variable order paths. We show how a class of multiple discrete delay differential…
Girsanov Theorem for Multifractional Brownian Processes
Fabian Harang, Torstein Nilssen, Frank Proske
In this article we will present a new perspective on the variable order fractional calculus, which allows for differentiation and integration to a variable order, i.e. one differen…