In previous chapters stochastic differential equations have been mentioned several times in an informal manner. For instance, if M is a continuous local martingale, its exponential e(M) satisfies the equality $$\mathcal{E}{(M)_t} = 1 + \int_0^t {\mathcal{E}{{(M)}_s}} d{M_s};$$ this can be stated: e(M) is a solution to the stochastic differential equation $${X_t} = 1 + \int_0^t {{X_s}d{M_s},} $$ which may be written in differential form $$d{X_t} = {X_t}d{M_t},{X_0} = 1.$$ We have even seen (Exercise (3.10) Chap. IV) that e(M) is the only solution to this equation. Likewise we saw in Sect. 2 Chap. VII, that some Markov processes are solutions of what may be termed stochastic differential equations.