We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention focused on noise generated by a Gaussian Ornstein Uhlenbeck process, going beyond usual telegraph noise, where random variables are consist only -1 1. Under first-order approximation BCH formula, master equation noisy der...

We decompose time-varying beta for stock into beta for continuous systematic risk and beta for discontinuous systematic risk. Brownian motion is assumed as nature of price movements in our modeling. Our empirical research is based on high-frequency data for stocks from Tehran Stock Exchange. Our market portfolio experiences 136 days out of 243 trading days with jumps which is a considerable rat...