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XIV: 24, 209-219, LNM 784 (1980)

**PELLAUMAIL, Jean**

Remarques sur l'intégrale stochastique (Stochastic calculus)

This is an exposition of stochastic integrals and stochastic differential equations for Banach space valued processes along the lines of Métivier-Pellaumail*Stochastic Integration* (1980), the class of semimartingales being defined by the Métivier-Pellaumail inequality (1413)

Keywords: Stochastic integrals, Stochastic differential equations, Métivier-Pellaumail inequality

Nature: Exposition

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XV: 38, 561-586, LNM 850 (1981)

**PELLAUMAIL, Jean**

Solutions faibles et semi-martingales (Stochastic calculus, General theory of processes)

From the author's summary: ``we consider a stochastic differential equation $dX=a(X)\,dZ$ where $Z$ is a semimartingale and $a$ is a previsible functional which is continuous for the uniform norm. We prove the existence of a weak solution for such an equation''. The important point is the definition of a weak solution: it turns out to be a ``fuzzy process'' in the sense of 1536, i.e., a fuzzy r.v. taking values in the Polish space of cadlag sample functions

Keywords: Stochastic differential equations, Weak solutions, Fuzzy random variables

Nature: Original

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XVI: 42, 469-489, LNM 920 (1982)

**PELLAUMAIL, Jean**

Règle maximale

Retrieve article from Numdam

Remarques sur l'intégrale stochastique (Stochastic calculus)

This is an exposition of stochastic integrals and stochastic differential equations for Banach space valued processes along the lines of Métivier-Pellaumail

Keywords: Stochastic integrals, Stochastic differential equations, Métivier-Pellaumail inequality

Nature: Exposition

Retrieve article from Numdam

XV: 38, 561-586, LNM 850 (1981)

Solutions faibles et semi-martingales (Stochastic calculus, General theory of processes)

From the author's summary: ``we consider a stochastic differential equation $dX=a(X)\,dZ$ where $Z$ is a semimartingale and $a$ is a previsible functional which is continuous for the uniform norm. We prove the existence of a weak solution for such an equation''. The important point is the definition of a weak solution: it turns out to be a ``fuzzy process'' in the sense of 1536, i.e., a fuzzy r.v. taking values in the Polish space of cadlag sample functions

Keywords: Stochastic differential equations, Weak solutions, Fuzzy random variables

Nature: Original

Retrieve article from Numdam

XVI: 42, 469-489, LNM 920 (1982)

Règle maximale

Retrieve article from Numdam