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XIV: 13, 118-124, LNM 784 (1980)

**ÉMERY, Michel**

Équations différentielles stochastiques. La méthode de Métivier-Pellaumail (Stochastic calculus)

Métivier-Pellaumail introduced the idea of an increasing process $(A_t)$ controlling a semimartingale $X$ as the property $$E[\,(sup_{t<T} \int_0^t H_s dX_s)^2\,] \le E[\,A_{T-}\,\int_0^{T-} H_s^2 dA_s\,]$$ for all stopping times $T$ and bounded previsible processes $(H_t)$. For a proof see 1414. Métivier-Pellaumail used this inequality to develop the theory of stochastic differential equations (including stability) without localization and pasting together at jump times. Here their method is applied to the topology of semimartingales

Comment: See 1352. A general reference on the Métivier-Pellaumail method can be found in their book*Stochastic Integration,* Academic Press 1980. See also He-Wang-Yan, *Semimartingale Theory and Stochastic Calculus,* CRC Press 1992

Keywords: Semimartingales, Spaces of semimartingales, Stochastic differential equations, Doob's inequality, Métivier-Pellaumail inequality

Nature: Original

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Équations différentielles stochastiques. La méthode de Métivier-Pellaumail (Stochastic calculus)

Métivier-Pellaumail introduced the idea of an increasing process $(A_t)$ controlling a semimartingale $X$ as the property $$E[\,(sup_{t<T} \int_0^t H_s dX_s)^2\,] \le E[\,A_{T-}\,\int_0^{T-} H_s^2 dA_s\,]$$ for all stopping times $T$ and bounded previsible processes $(H_t)$. For a proof see 1414. Métivier-Pellaumail used this inequality to develop the theory of stochastic differential equations (including stability) without localization and pasting together at jump times. Here their method is applied to the topology of semimartingales

Comment: See 1352. A general reference on the Métivier-Pellaumail method can be found in their book

Keywords: Semimartingales, Spaces of semimartingales, Stochastic differential equations, Doob's inequality, Métivier-Pellaumail inequality

Nature: Original

Retrieve article from Numdam