14 papers · 1 filter
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…
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…
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…
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…