instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Dynamics of SDEs driven by a Fractional Brownian Motion with Hurst parameter H > 1/2
Seminario de Ecuaciones Diferenciales y Análisis Numérico
In this talk we consider a pathwise approach to stochastic integration. As an example we introduce the Fractional Brownian Motion (FBM) which is in general not a semimartingale and hence it is not possible to define an Itô integral. Hence, we show the definition of the Young integral using the Hölder regularity of the FBM. Then, we consider Stochastic Evolution Equations in mild form, show the existence of a global solution under suitable conditions on the coefficients and derive dyamic properties.