The auto-correlation function and the cross-correlation function of an autonomous stochastic system with time delays are investigated. We obtain the distribution curves of the auto-correlation function Cx(s) and Cy(s), and the cross-correlation function Cxy(s) and Cyx(s) of the stochastic...

In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo...

Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent process and transformation of the new system, the deviation from the Monte Carlo price is seen to be...

Many real-world networks exhibit community structure where vertices belong to one or more communities. Recent studies show that community structure plays an import role in epidemic spreading. In this paper, we investigate how the extent of overlap among communities affects epidemics. In order to...