## View abstract

### Session S17 - Stochastic Systems: Analysis, Numerics and Applications

Friday, July 16, 12:00 ~ 12:35 UTC-3

## Stratonovich type integration with respect to fractional Brownian motion with Hurst parameter less than 1/2

### Jorge A. León

#### Departamento de Control Automático, Cinvestav-IPN, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak5a5ea284476076f153416a881b988354').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy5a5ea284476076f153416a881b988354 = 'jl&#101;&#111;n' + '&#64;'; addy5a5ea284476076f153416a881b988354 = addy5a5ea284476076f153416a881b988354 + 'ctrl' + '&#46;' + 'c&#105;nv&#101;st&#97;v' + '&#46;' + 'mx'; var addy_text5a5ea284476076f153416a881b988354 = 'jl&#101;&#111;n' + '&#64;' + 'ctrl' + '&#46;' + 'c&#105;nv&#101;st&#97;v' + '&#46;' + 'mx';document.getElementById('cloak5a5ea284476076f153416a881b988354').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy5a5ea284476076f153416a881b988354 + '\'>'+addy_text5a5ea284476076f153416a881b988354+'<\/a>';

In this talk, we introduce a Stratonovich type integral with respect to fractional Brownian motion with Hurst parameter $H\in(0,1/2)$. Then, we study an It\^o's type formula, the relation between this integral and an extension of the divergence operator, and the existence of a unique solution to some Stratonovich stochastic differential equations. Towards this end, roughly speaking, we only need to use the norm of the space $L^2(\Omega\times[0,T])$ instead of a norm of a Sobolev space given by the Malliavin calculus.