Stochastic Simulation and Monte Carlo Methods

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By: Andreas Helander

Stochastic models, Stochastic methods

In these lecture notes we will work through three different computational problems from different application areas. We will simulate the irregular motion of a particle in an environment of smaller solvent molecules, we will study a biochemical control network and we will compute a numerical approximation to a high dimensional integral. Even though these three problems are different, and the way we will solve them will be different, they have one thing in common. In each case we will use a Monte Carlo method.

There is not a single definition of a Monte Carlo method, but they have in common that they make use of random sampling to compute the result. The algorithms typically rely on pseudo random numbers, computer generated numbers mimicking true random numbers, to generate a realization, one possible outcome of a process. All outcomes do not have to be equally probable, and by repeating the procedure with different random numbers as input, one gathers data corresponding to the modeled process. On this data, one may then perform a statistical analysis in order to answer different questions about the process.

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