Fabian Andsem Harang

Harang, Fabian Andsem; Tindel, Samy & Wang, Xiaohua (2022)

Volterra equations driven by rough signals 2: higher order expansions

Stochastics and Dynamics Doi: 10.1142/S0219493723500028 - Full text in research archive

Galeati, Lucio; Harang, Fabian Andsem & Mayorcas, Avi (2022)

Distribution dependent SDEs driven by additive continuous noise

Electronic Journal of Probability (EJP), 27, s. 1- 38. Doi: 10.1214/22-EJP756 - Full text in research archive

Harang, Fabian Andsem; Nilssen, Torstein & Proske, Frank Norbert (2022)

GIRSANOV THEOREM FOR MULTIFRACTIONAL BROWNIAN PROCESSES

Stochastics: An International Journal of Probability and Stochastic Processes Doi: 10.1080/17442508.2022.2027948 - Full text in research archive

Galeati, Lucio & Harang, Fabian Andsem (2022)

Regularization of multiplicative SDEs through additive noise

The Annals of Applied Probability, 32(5), s. 3930- 3963. Doi: 10.1214/21-AAP1778 - Full text in research archive

Harang, Fabian Andsem & Perkowski, Nicolas (2021)

C ∞ - regularization of ODEs perturbed by noise

Stochastics and Dynamics, 21(8) Doi: 10.1142/S0219493721400104 - Full text in research archive

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 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

Harang, Fabian Andsem & Tindel, Samy (2021)

Volterra Equations Driven by Rough Signals

Stochastic Processes and their Applications, 142, s. 34- 78. Doi: 10.1016/j.spa.2021.08.001 - Full text in research archive

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 parameter functions defined on the simplex called Volterra paths. These paths are used to construct a so-called Volterra-signature, analogously to the signature used in Lyon’s theory of rough paths. We provide a detailed algebraic and analytic description of this object. Interestingly, the Volterra signature does not have a multiplicative property similar to the classical signature, and we introduce an integral product behaving like a convolution extending the classical tensor product. We show that this convolution product is well defined for a large class of Volterra paths, and we provide an analogue of the extension theorem from the theory of rough paths (which guarantees in particular the existence of a Volterra signature). Moreover the concept of convolution product is essential in the construction of Volterra controlled paths, which is the natural class of processes to be integrated with respect to the driving noise in our situation. This leads to a rough integral given as a functional of the Volterra signature and the Volterra controlled paths, combined through the convolution product. The rough integral is then used in the construction of unique solutions to Volterra equations driven by Hölder noises with singular kernels. An example concerning Brownian noises and a singular kernel is treated.

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), 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, 12(3), s. 1257- 1284. Doi: 10.1137/20M135902X - Full text in research archive

Harang, Fabian Andsem; Lagunas, Marc & Ortiz-Latorre, Salvador (2021)

Self-Exciting Multifractional Processes

Journal of Applied Probability, 58(1), s. 22- 41. Doi: 10.1017/jpr.2020.88 - Full text in research archive

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, 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 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 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

Harang, Fabian Andsem (2020)

Volterra Equations driven by Rough Noise

[Academic lecture]. Seminar for Probability group at Université Nice-Sophia-Antipolis.

Harang, Fabian Andsem (2020)

Volterra Equations Driven by Rough Signals

[Academic lecture]. Seminar For Berlin Rough Paths Group.

Harang, Fabian Andsem (2020)

Infinitely regularising paths and regularisation by noise

[Academic lecture]. Oxford Stochastic Analysis and Mathematical Finance Seminar.

Harang, Fabian Andsem (2019)

Volterra equations driven by rough signals (2)

[Academic lecture]. CSA2019 - Conference in Stochastic Analysis - Risør.

Harang, Fabian Andsem (2019)

Volterra equations driven by rough signals

[Academic lecture]. Berlin -Oxford meeting, WIAS Berlin.

Harang, Fabian Andsem (2019)

A multi parameter sewing lemma, and applications

[Academic lecture]. Seminar at NTNU Trondhiem.

Harang, Fabian Andsem (2019)

A Multiparameter Sewing Lemma with applications

[Academic lecture]. Seminar at Purdue University, Indiana, USA.