Stochastic di erential equations play an important role in modern science, including engineering, physics, computer science and nance. It has... Show moreStochastic di erential equations play an important role in modern science, including engineering, physics, computer science and nance. It has been shown that numerically solving stochastic di erential equation is a productive methodto deal with such problems. In this work, we try to analyze the procedure of numerically computing the mean exit time of some stochastic processes from a given boundary using Monte Carlo simulations. The two methods, including the Euler-Maruyama Method and Milstein's higher order method, will be explained and used extensively when we simulate paths of the random process. The simulated processes generated through the methods will then be used to identify the exit times. Later we use the average of the exit times as a numerical solution of Mean Exit Time. We compare the e ciency of the above two methods by evaluating their computational complexity and CPU cost of reaching the same level of accuracy. M.S. in Applied Mathematics, May 2016 Show less
