**Abstract**

The article studies a novel approach of inflation modeling in economics. We utilize a stochastic differential equation (SDE) of the form *dXt* ¼ *a X*ð Þ , *t dt* þ *b X*ð Þ , *<sup>t</sup> dBH <sup>t</sup>* , where *dB<sup>H</sup> <sup>t</sup>* is a fractional Brownian motion in order to model inflationary dynamics. Standard economic models do not capture the stochastic nature of inflation in the Eurozone. Thus, we develop a new stochastic approach and take into consideration fractional Brownian motions as well as Lévy processes. The benefits of those stochastic processes are the modeling of interdependence and jumps, which is equally confirmed by empirical inflation data. The article defines and introduces the rules for stochastic and fractional processes and elucidates the stochastic simulation output.

**Keywords:** inflation, dynamics, modeling, stochastic differential equation, fractional Brownian motion, Lévy process, jump-diffusion
