Zobrazeno 1 - 10
of 167
pro vyhledávání: '"60l20"'
We introduce a canonical way of performing the joint lift of a Brownian motion $W$ and a low-regularity adapted stochastic rough path $\mathbf{X}$, extending [Diehl, Oberhauser and Riedel (2015). A L\'evy area between Brownian motion and rough paths
Externí odkaz:
http://arxiv.org/abs/2412.21192
The universal limit theorem is a central result in rough path theory, which has been proved for: (i) rough paths with roughness $\frac{1}{3}< \alpha \leq \frac{1}{2}$; (ii) geometric rough paths with roughness $0< \alpha \leq 1$; (iii) branched rough
Externí odkaz:
http://arxiv.org/abs/2412.16479
We study stochastic optimal control of rough stochastic differential equations (RSDEs). This is in the spirit of the pathwise control problem (Lions--Souganidis 1998, Buckdahn--Ma 2007; also Davis--Burstein 1992), with renewed interest and recent wor
Externí odkaz:
http://arxiv.org/abs/2412.05698
The aim of the paper is to show the probabilistically strong well-posedness of rough differential equations with distributional drifts driven by the Gaussian rough path lift of fractional Brownian motion with Hurst parameter $H\in(1/3,1/2)$. We assum
Externí odkaz:
http://arxiv.org/abs/2412.01645
Autor:
Pang, Peter H. C.
In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^\alpha([0,T];\mathbb{R}^d)$, $\frac13 < \alpha \le \frac12$, using a splitting-up scheme. We show convergence of our scheme to s
Externí odkaz:
http://arxiv.org/abs/2412.00432
We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a priori bounds f
Externí odkaz:
http://arxiv.org/abs/2411.04590
In this paper we generalize Krylov's theory on parameter-dependent stochastic differential equations to the framework of rough stochastic differential equations (rough SDEs), as initially introduced by Friz, Hocquet and L\^e. We consider a stochastic
Externí odkaz:
http://arxiv.org/abs/2409.11330
Autor:
Diamantakis, Theo, Hu, Ruiao
The Stochastic Advection by Lie Transport is a variational formulation of stochastic fluid dynamics introduced to model the effects of unresolved scales, whilst preserving the geometric structure of ideal fluid flows. In this work, we show that the S
Externí odkaz:
http://arxiv.org/abs/2409.10408
Autor:
Bielert, Franziska
We prove a rough It\^o formula for path-dependent functionals of $\alpha$-H\"older continuous paths for $\alpha\in(0,1)$. Our approach combines the sewing lemma and a Taylor approximation in terms of path-dependent derivatives.
Externí odkaz:
http://arxiv.org/abs/2409.02532
Autor:
Allan, Andrew L., Pieper, Jost
We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c\`adl\`ag setting. In particular, we define rough stochast
Externí odkaz:
http://arxiv.org/abs/2408.06978