Prior to 1961, he worked as a member of a group of mathematicians united around E. B. Dynkin who were developing the theory of Markov processes.
In the same thesis he considered the problem of applying Markov processes to the solution of partial differential equations.
In his papers on stochastic differential equations he determined the conditions when the discontinuity of the coefficients does not prevent the solution from being unique.
Girsanov became an advocate of mathematical economics, actively defending it against the opponents of quantitative methods.
He also maintained his interest in theoretical mathematics developing the functional analysis required for optimisation problems.
Girsanov died on 16 March 1967 at the age of 32 as a result of an accident during a hike in the Sayan Mountains.