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XIX: 22, 271-274, LNM 1123 (1985)

**LÉANDRE, Rémi**

Flot d'une équation différentielle stochastique avec semimartingale directrice discontinue (Stochastic calculus)

Given a good s.d.e. of the form $dX=F\circ X_- dZ$, $X_{t-}$ is obtained from $X_t$ by computing $H_z(x) = x+F(x)z$, where $z$ stands for the jump of $Z$. Call $D$ (resp. $I$ the set of all $z$ such that $H_z$ is a diffeomorphism (resp. injective). It is shown that the flow associated to the s.d.e. is made of diffeomorphisms (respectively is one-to-one) iff all jumps of $Z$ belong to $D$ (resp. $I$)

Keywords: Stochastic differential equations, Flow of a s.d.e.

Nature: Original

Retrieve article from Numdam

Flot d'une équation différentielle stochastique avec semimartingale directrice discontinue (Stochastic calculus)

Given a good s.d.e. of the form $dX=F\circ X_- dZ$, $X_{t-}$ is obtained from $X_t$ by computing $H_z(x) = x+F(x)z$, where $z$ stands for the jump of $Z$. Call $D$ (resp. $I$ the set of all $z$ such that $H_z$ is a diffeomorphism (resp. injective). It is shown that the flow associated to the s.d.e. is made of diffeomorphisms (respectively is one-to-one) iff all jumps of $Z$ belong to $D$ (resp. $I$)

Keywords: Stochastic differential equations, Flow of a s.d.e.

Nature: Original

Retrieve article from Numdam