Stochastic methods for finance are methods which use mathematical and expecially statistical tools to forecast values or to have a signal of relevant approaching events.
The most used statistical tool is the regression (linear and non linear), which builds a model of current prices based on previous prices and volumes. This kind of models has a very reliable measure called R-square which gives an indication of how well the model predicts yesterday's prices using information from previous days. Obviously no guarantee exists for tomorrow's prices, expecially in presence of shocks due to sudden change of economical situations. Therefore it is always a good technique to couple regression models with natural language news analizers. Other more sophisticated models exists, which take into consideration several layers of interaction to better reflect economic reality.
Other stochastic methods are genetic algorithms, which use a self-adaptive strategy derived from biology to predict prices, and neural networks, which use instead a network of simple nodes which auto-builds an economical model for prices.