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• Harang, Fabian Andsem & Ling, Chengcheng (2021). Regularity of Local Times Associated with Volterra–Lévy Processes and Path-Wise Regularization of Stochastic Differential Equations. Journal of theoretical probability. ISSN 0894-9840. doi: 10.1007/s10959-021-01114-4. Full text in Research Archive
• Harang, Fabian Andsem & Catellier, Rémi (2021). Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation. arXiv.org. ISSN 2331-8422.
• Harang, Fabian Andsem & Tindel, Samy (2021). Volterra Equations Driven by Rough Signals. Stochastic Processes and their Applications. ISSN 0304-4149. doi: 10.1016/j.spa.2021.08.001.
• Harang, Fabian Andsem & Benth, Fred Espen (2021). Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications . Electronic Journal of Probability (EJP). ISSN 1083-6489. 26. doi: 10.1214/21-EJP683. Full text in Research Archive
• Bayer, Christian; Harang, Fabian Andsem & Pigato, Paolo (2021). Log-modulated rough stochastic volatility models. SIAM Journal on Financial Mathematics. ISSN 1945-497X. 12(3), p. 1257–1284. doi: 10.1137/20M135902X.
• Harang, Fabian Andsem; Lagunas, Marc & Ortiz-Latorre, Salvador (2021). Self-Exciting Multifractional Processes. Journal of Applied Probability. ISSN 0021-9002. 58(1), p. 22–41. doi: 10.1017/jpr.2020.88.
• 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 & 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.

• 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), p. 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 (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.
• 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 regularizing paths, and regularization by noise.
• Harang, Fabian Andsem (2020). C^\infty regularization of ODEs perturbed by noise.
• Harang, Fabian Andsem (2020). Volterra Equations driven by Rough Noise.
• Harang, Fabian Andsem (2020). Volterra Equations Driven by Rough Signals.
• Harang, Fabian Andsem (2020). Infinitely regularising paths and regularisation by noise.
• 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 (2019). Volterra equations driven by rough signals (2).
• Harang, Fabian Andsem (2019). Volterra equations driven by rough signals.
• Harang, Fabian Andsem (2019). A multi parameter sewing lemma, and applications.
• Harang, Fabian Andsem (2019). A Multiparameter Sewing Lemma with applications.
• Harang, Fabian Andsem (2018). Stability and Regularization of Stochastic Equations Driven by Fractional and Multifractional Noise. Universitetet i Oslo. ISSN 1501-7710.

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