Fabian Andsem Harang

• Harang, Fabian Andsem & Catellier, Rémi (2021). Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation. arXiv.org.  ISSN 2331-8422.
• Amine, Oussama; Coffie, Emmanuel; Harang, Fabian Andsem & Proske, Frank Norbert (2020). Bismut–Elworthy–Li formula, singular SDEs, fractional Brownian motion, Malliavin calculus, stochastic flows, stochastic volatility. Communications in Mathematical Sciences.  ISSN 1539-6746.  18(7), s 1863- 1890 . doi: 10.4310/CMS.2020.v18.n7.a3
• Harang, Fabian Andsem (2020). An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi-parameter Young fields. Stochastics and Partial Differential Equations: Analysis and Computations.  ISSN 2194-0401. . doi: 10.1007/s40072-020-00184-5
• Harang, Fabian Andsem; Bayer, Christian & Pigato, Paolo (2020). Log-modulated rough stochastic volatility models. arXiv.org.  ISSN 2331-8422. . doi: 10.2139/ssrn.3668973
• Harang, Fabian Andsem & Benth, Fred Espen (2020). Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications. arXiv.org.  ISSN 2331-8422.
• Harang, Fabian Andsem & Galeati, Lucio (2020). Regularization of multiplicative SDEs through additive noise. arXiv.org.  ISSN 2331-8422.
• Harang, Fabian Andsem & Ling, Chengcheng (2020). Regularity of Local times associated to Volterra-Lévy processes and path-wise regularization of stochastic differential equations. arXiv.org.  ISSN 2331-8422. Show summary

  We investigate the space-time regularity of the local time associated to Volterra-Lévy processes, including Volterra processes driven by α-stable processes for α∈(0,2]. We show that the spatial regularity of the local time for Volterra-Lévy process is P-a.s. inverse proportionally to the singularity of the associated Volterra kernel. We apply our results to the investigation of path-wise regularizing effects obtained by perturba\Ption of ODEs by a Volterra-Lévy process which has sufficiently regular local time. Following along the lines of \cite{HarangPerkowski2020}, we show existence, uniqueness and differentiablility of the flow associated to such equations.

• Harang, Fabian Andsem & Mayorcas, Avi (2020). PATHWISE REGULARISATION OF SINGULAR INTERACTING PARTICLE SYSTEMS AND THEIR MEAN FIELD LIMITS. arXiv.org.  ISSN 2331-8422.
• Harang, Fabian Andsem & Perkowski, Nicolas (2020). C-infinity regularization of ODEs perturbed by noise. arXiv.org.  ISSN 2331-8422.
• Harang, Fabian Andsem & Tindel, Samy (2020). Volterra Equations Driven by Rough Signals. arXiv.org.  ISSN 2331-8422.
• Harang, Fabian Andsem (2019). Differential Equations Driven by Variable Order Hölder Noise, and the Regularizing Effect of Delay. Stochastics: An International Journal of Probability and Stochastic Processes.  ISSN 1744-2508. . doi: 10.1080/17442508.2019.1602130
• Harang, Fabian Andsem; Lagunas, Marc & Ortiz-Latorre, Salvador (2019). Self-Exciting Multifractional Processes. arXiv.org.  ISSN 2331-8422.
• Amine, Oussama; Coffie, Emmanuel; Harang, Fabian Andsem & Proske, Frank Norbert (2018). A Bismut-Elworthy-Li Formula for Singular SDE's Driven by a Fractional Brownian Motion and Applications to Rough Volatility Modeling. arXiv.org.  ISSN 2331-8422.
• Harang, Fabian Andsem; Proske, Frank Norbert & Nilssen, Torstein Kastberg (2017). Girsanov Theorem for Multifractional Brownian Processes. arXiv.org.  ISSN 2331-8422. Full text in Research Archive.

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• Harang, Fabian Andsem (2020). Infinitely regularising paths and regularisation by noise.
• Harang, Fabian Andsem (2020). C^\infty regularization of ODEs perturbed by noise.
• Harang, Fabian Andsem (2020). Infinitely regularizing paths, and regularization by noise.
• Harang, Fabian Andsem (2020). Volterra Equations Driven by Rough Signals.
• Harang, Fabian Andsem (2020). Volterra Equations driven by Rough Noise.
• Harang, Fabian Andsem (2019). A Multiparameter Sewing Lemma with applications.
• Harang, Fabian Andsem (2019). A multi parameter sewing lemma, and applications.
• Harang, Fabian Andsem (2019). Volterra equations driven by rough signals.
• Harang, Fabian Andsem (2019). Volterra equations driven by rough signals (2).
• Lagunas Merino, Marc; Harang, Fabian Andsem & Ortiz-Latorre, Salvador (2019). Self-Exciting Multifractional Processes (SEM) Processes. Show summary

  Abstract. 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 phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this through a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as give bounds on the p-order moments, for all p>=1. We show convergence of an Euler-Maruyama scheme for the process, and also give the rate of convergence, which is depending on the self-exciting dynamics of the process. Moreover, we discuss different applications of this process, and give examples of different functions to model self-exciting behavior.

• Harang, Fabian Andsem (2018). Stability and Regularization of Stochastic Equations Driven by Fractional and Multifractional Noise. Series of dissertations submitted to the Faculty of Mathematics and Natural Sciences, University of Oslo.. 2055.

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