# Spatial rough path lifts of stochastic convolutions

@article{Friz2012SpatialRP, title={Spatial rough path lifts of stochastic convolutions}, author={Peter K. Friz and Benjamin Gess and Archil Gulisashvili and Sebastian Riedel}, journal={arXiv: Probability}, year={2012} }

We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their variance function. The motivation for this type of conditions comes from recent work of Hairer [CPAM,2011]. Our results allow to construct rough paths lifts of solutions to a class of fractional stochastic heat equations with additive, possibly colored Wiener noise with respect to their space variable.

## 4 Citations

### Large deviation principle for certain spatially lifted Gaussian rough path

- Mathematics
- 2012

In rough stochastic PDE theory of Hairer type, rough path lifts with respect to the space variable of two-parameter continuous Gaussian processes play a main role. A prominent example of such…

### Approximating Rough Stochastic PDEs

- MathematicsCommunications on Pure and Applied Mathematics
- 2013

We study approximations to a class of vector‐valued equations of Burgers type driven by a multiplicative space‐time white noise. A solution theory for this class of equations has been developed…

### PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES

- MathematicsForum of Mathematics, Pi
- 2015

We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough…

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We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough…

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This paper aims to provide a systematic approach to the treatment of differential equations of the type
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