Monte Carlo methods: are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms. Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a computer, utilizing many techniques of computer simulation.
and another defintion -
A computer-driven model that simulates a sufficiently large number of potential interest rate paths to value a security on the basis of performance along a composite of these paths. Monte Carlo is considered the most sensitive measure of valuing interest rate-sensitive debt instruments based on historical interest rate environments and their probability of repeating. Monte Carlo has become the standard for evaluating mortgage-backed and asset-backed securities.
Markov Chain: A stochastic process with a finite number of states in which the probability of occurrence of a future state is conditional only upon the current state; past states are inconsequential. In meteorology, Markov chains have been used to describe a raindrop size distribution in which the state at time step n + 1 is determined only by collisions between pairs of drops comprising the size distribution at time step n. (from here)
Also see wiki - there are good links at the bottom. The Markov Chain Monte Carlo mentioned at the bottom is used by Kingston, Maier and Lambert(2006)
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