Hi: That statement is made understand the assumption that a stock's return is composed of a drift term and a random component.

$\triangle r_t = \mu \times dt + \sigma \times dW_t$

where $dW_t$ denotes the derivative of brownian motion ( note that the derivative really doesn't exist but they say that anyway ) and is often referred to as white noise.

Brownian motion has increments that are independent and it's serial correlation, $corr(W_s,W_t) = min(s,t)$ but only for the same stock. For different stocks, it's zero. This info will be explained with all the details ( regarding quadratic variation, Ito's Lemma etc ) in any decent probability or finance book.

For a gentle intro, Mikosch's "Elementary Stochastic Calculus With Finance in View" is good but then there are more advanced ones like Karatzas and Schreve or Protter etc. It depends on your background and what you want to know. The levels can vary a lot.

Hi: That statement is made understand the assumption that a stock's return is composed of a drift term and a random component and the stock price, $S_t$ is then said to follow geometric brownian motion:

$ dS_t = \mu \times S_t \times dt + \sigma \times S_t \times dW_t$

In above, $dW_t$ denotes the derivative of brownian motion ( note that the derivative really doesn't exist but they say that anyway ) and is often referred to as white noise.

Brownian motion has increments that are independent and it's serial correlation, $corr(W_s,W_t) = min(s,t)$ but only for the same stock. For different stocks, it's zero. This info will be explained with all the details ( regarding quadratic variation, Ito's Lemma etc ) in any decent probability or finance book.

For a gentle intro, Mikosch's "Elementary Stochastic Calculus With Finance in View" is good but then there are more advanced ones like Karatzas and Schreve or Protter etc. It depends on your background and what you want to know. The levels can vary a lot.

Hi: That statement is made understand the assumption that a stock's return is composed of a drift term and a random component.

$\triangle r_t = \mu \times dt + \sigma \times dW_t$

where $dW_t$ is viewed as the derivative of brownian motion ( note that the derivative really doesn't exist but they say that anyway ) and is often referred to as white noise.

Brownian motion has increments that are independent and it's serial correlation, $corr(W_s,W_t) = min(s,t)$ but only for the same stock. For different stocks, it's zero. This info will be explained with all the details ( regarding quadratic variation, Ito's Lemma etc ) in any decent probability or finance book.

For a gentle intro, Mikosch's "Elementary Stochastic Calculus With Finance in View" is good but then there are more advanced ones like Karatzas and Schreve or Protter etc. It depends on your background and what you want to know. The levels can vary a lot.

Hi: That statement is made understand the assumption that a stock's return is composed of a drift term and a random component.

$\triangle r_t = \mu \times dt + \sigma \times dW_t$

where $dW_t$ denotes the derivative of brownian motion ( note that the derivative really doesn't exist but they say that anyway ) and is often referred to as white noise.

Brownian motion has increments that are independent and it's serial correlation, $corr(W_s,W_t) = min(s,t)$ but only for the same stock. For different stocks, it's zero. This info will be explained with all the details ( regarding quadratic variation, Ito's Lemma etc ) in any decent probability or finance book.

For a gentle intro, Mikosch's "Elementary Stochastic Calculus With Finance in View" is good but then there are more advanced ones like Karatzas and Schreve or Protter etc. It depends on your background and what you want to know. The levels can vary a lot.