ABSTRACT
This chapter deals with the basics of stochastic analysis. A probability distribution on Rn is a probability measure on the σ-algebra ofBorel subsets; i.e., it assigns to every Borel set a probability, so that the probability axioms are satisfied. Every random vector gives rise to a probability distribution. On the other hand, for any probability distribution, one can find a random vector with that distribution. In general, the probability distribution of a random vector is not uniquely defined by the set of probability distributions of its components. Some basic properties of a Wiener process w(t) are: sample paths are continuous; sample paths are non-differentiable and they are not absolutely continuous; and it is a Markov process. The chapter also presents a special case of the celebrated Girsanov’s theorem.
