## Temps d’explosion d’équations différentielles stochastiques du type Doléans-Dade. (Explosion times for solutions of Doléans-Dade stochastic differential equations).(French)Zbl 0752.60048

For Doléans-Dade equations $$X_ t=x+\int^ t_ 0 A(X)_ s dZ_ s$$ of the continuous martingale $$Z$$, $$P(T(\omega,x)=\infty$$, $$\forall x\in R^ d)=1$$ is proved for the explosion time $$T(\infty,x)$$ if the operator $$A$$ is at most of linear growth and if for any stopping time $$T$$, any $$u,v\in\{\omega:\sup_{[0,T]}|\omega_ t|\leq n\}$$ for each $$n$$, $\sup_{[0,T]}| A(u)-A(v)|\leq (\log n)^{1/2}\sup_{[0,T]}| u-v|$ holds.

### MSC:

 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G44 Martingales with continuous parameter
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