Stochastic Process Examples I was wondering if people could give me examples of how stochastic processes are seen and used in research in real life.
 A: Of course you have many application in "real life" problems, since all the motivation about the probability theory is to modeling this kind of problems.
You have stock markets applications how Brady Trainor said but not only this.
Stochastic process can be used to model the number of people or information data (computational network, p2p etc) in a queue over time where you suppose for example that the number of persons or information arrives is a poisson process.
Also in biology you have applications in evolutive ecology theory with birth-death process. In neuroscience, considering noise perturbations of ionic and chemical potential in neurons membrane.
In game theory, when you work with differential games for instance, which are a general framework for modeling many different "real word" problems in economy, computer science and others.
In optimisation and control of systems (stochastic control theory), were you typically model your uncertainty about the system interaction with the environment by stochastic process. Just to try to make it more concrete, automatic systems in general like for example the autopilot for cars ( you can obviously extend it for any other vehicle  from mini robots to space shuttles) 
In physics, more precisely in statistical physics formalisme and in complex systems.
It's just to try to give you a better idea about some possible applications and of course it's not an exhaustive list. I expect it can guide you for your research on the web.
A: You can apply the concepts to pricing stock options. A stock option includes items such as puts and calls. 
Let's consider what a call option is, based on some stock, let's say in Atari. A call agreement will include the type of stock (Atari), a strike price, a premium, and the date of expiration, call it T. The strike price is what the call allows us, or gives us the right, to buy at strike, at expiration. 
We can hold the option, then, at time T, if the strike price is lower than whatever the price is at that time, we can exercise our right to buy at strike, than sell it for the price at that time, thus giving a profit. If the price had dropped below strike, we would simply not exercise the option, and let it expire. Thus, we cannot lose. 
Therefore, we must have payed some positive premium for this call option. 
The future price is random. We must use stochastics to price the option. 
