Corpus ID: 214667009

# Variability of paths and differential equations with $BV$-coefficients

@article{Hinz2020VariabilityOP,
title={Variability of paths and differential equations with \$BV\$-coefficients},
author={Michael Hinz and Jonas M. Tolle and Lauri Viitasaari},
journal={arXiv: Probability},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Probability
• We define compositions $\varphi(X)$ of H\"older paths $X$ in $\mathbb{R}^n$ and functions of bounded variation $\varphi$ under a relative condition involving the path and the gradient measure of $\varphi$. We show the existence and properties of generalized Lebesgue-Stieltjes integrals of compositions $\varphi(X)$ with respect to a given H\"older path $Y$. These results are then used, together with Doss' transform, to obtain existence and, in a certain sense, uniqueness results for differential… CONTINUE READING

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 104 REFERENCES

## Rough differential equations with power type nonlinearities

• Mathematics
• 2016
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## On the regularity of stochastic currents, fractional Brownian motion and applications to a turbulence model

• Mathematics
• 2007
VIEW 1 EXCERPT

## ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERALIZED DRIFT ∗

• Mathematics
• 2014
VIEW 1 EXCERPT

## Local invertibility of Sobolev functions

• Mathematics
• 1995
VIEW 1 EXCERPT

## BILIPSCHITZ MAPPINGS WITH DERIVATIVES OF BOUNDED VARIATION

VIEW 1 EXCERPT

## Joint continuity of the local times of fractional Brownian sheets

• Mathematics
• 2008
VIEW 1 EXCERPT

## The normalized numerical range and the Davis-Wielandt shell

• Mathematics
• 2017

## Local Invertibility in Sobolev Spaces with Applications to Nematic Elastomers and Magnetoelasticity

• Mathematics
• 2017

## Integration with respect to fractal functions and stochastic calculus. I

VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

## Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes

• Mathematics
• 2016
VIEW 3 EXCERPTS