# Almost sure diffusion approximation in averaging via rough paths theory

@inproceedings{Friz2021AlmostSD, title={Almost sure diffusion approximation in averaging via rough paths theory}, author={Peter K. Friz and Yuri Kifer}, year={2021} }

The paper deals with the fast-slow motions setups in the continuous time dX (t) dt = 1 ε σ(Xε(t))ξ(t/ε2) + b(Xε(t)), t ∈ [0, T ] and the discrete time XN ((n + 1)/N) = XN (n/N) + N σ(XN (n/N))ξ(n)) + Nb(XN (n/N))ξ(n), n = 0, 1, ..., [TN ] where σ and b are smooth matrix and vector functions, respectively, ξ is a centered stationary vector stochastic process and ε, 1/N are small parameters. We derive, first, estimates in the strong invariance principles for sums SN (t) = N −1/2 ∑ 0≤k<[Nt] ξ(k…

## One Citation

### Some strong limit theorems in averaging

- Mathematics
- 2022

. The paper deals with the fast-slow motions setups in the discrete time X ε (( n + 1) ε ) = X ε ( nε ) + εB ( X ε ( nε ) ,ξ ( n )), n = 0 , 1 ,..., [ T/ε ] and the continuous time dX ε ( t ) dt = B…

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