Fabian Andsem Harang

• 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.
• 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 (2018). An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi parameter Young fields. 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. Fulltekst i vitenarkiv.

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• 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. Vis sammendrag

  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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