6. Stochastic differential equations

6.1 Introduction

Informally speaking, an ordinary differential equation perturbed by a stochastic term is called a stochastic differential equation. More precisely, it's an equation of the following type: $d X_{t} = b (t, X) d t + σ (t, X_{t}) d W_{t}, X_{0} = x_{0}$

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References

(1) - DURETT (R.) - Brownian motion and martingale analysis - . Wadsworth Advanced Books and Software (1984).
(2) - DURETT (R.) - Stochastics calculus. - Probability and Stochastic Series, CRC Press (1996).
(3)...

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