Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/2
By Yaozhong Hu David Nualart. 2006
119 citations recorded by the source corpus.
We derive estimates for the solutions to differential equations driven by a H\"older continuous function of order $\beta>1/2$. As an application we deduce the existence of moments for the solutions to stochastic partial differential equations driven by a fractional Brownian motion with Hurst parameter $H>{1/2}$.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/99b05a6a2259ec333ffcf2724aa45bacdff6d855
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
- David Nualart
- Peter K. Friz
- Christian Litterer
- Samy Tindel
- T. Cass
- Nicolas Victoir
- Martin Hairer
- Khoa Le
In Finance
- Peter K. Friz
- Martin Hairer
- Samy Tindel
- T. Cass
- David Nualart
- Yaozhong Hu
- Nicolas Victoir
- Christian Litterer
Citations in the corpus
- A stochastic sewing lemma and applications (2018, background): “[6, 26]) and of the functional A (Corollary 3.”
- Smoothness of the density for solutions to Gaussian rough differential equations (2012, background): “For the case where X is fractional Brownian motion, this question was first addressed by Nualart and Hu [25], where the authors show the existence and smoothness of the density when the vector fields are elliptic, and the driving Gaussian”
- Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion (2009, background): “This result requires also the existence of moments for the iterated derivatives, which has been established in [4].”
- Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, methodology): “This result was first proved by Lyons [14], using Young integrals (see [33]) and p-variation estimates, and later by Nualart and Rascanu [25], using fractional calculus; see [34].”
- Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion (2012, methodology): “The estimates on the solution (xt)t∈[0,T ] obtained in [25] were improved in [19], Theorem 3.”
- Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, methodology): “Some of our estimates appear as special case in previous works, for instance in [131] in the "Young" case of 1-Hölder paths with ∈ [1 2).”
- Rough path analysis via fractional calculus (2006, background): “Further results have been obtained in [6] along the lines of the present paper.”