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 I. Basic math.
 1 Conditional probability.
 2 Normal distribution.
 3 Brownian motion.
 4 Poisson process.
 5 Ito integral.
 6 Ito calculus.
 7 Change of measure.
 8 Girsanov's theorem.
 A. Change of measure-based verification of Girsanov's theorem statement.
 B. Direct proof of Girsanov's theorem.
 9 Forward Kolmogorov's equation.
 10 Backward Kolmogorov's equation.
 11 Optimal control, Bellman equation, Dynamic programming.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Girsanov's theorem.

n this section we obtain the inverse result to the statement ( Transformation of SDE under change of measure ). Suppose is a standard Brownian motion adapted to a filtration and the process is given by where is some -adapted process. We wish to find a process , such that the is a standard Brownian motion with respect to the defined according to the formula ( Definition of change of measure ).

 A. Change of measure-based verification of Girsanov's theorem statement.
 B. Direct proof of Girsanov's theorem.
 Notation. Index. Contents.