Quick search | Browse volumes | |

XIV: 19, 161-172, LNM 784 (1980)

**JACOD, Jean**

Intégrales stochastiques par rapport à une semi-martingale vectorielle et changements de filtration (Stochastic calculus, General theory of processes)

Given a square integrable vector martingale $M$ and a previsible vector process $H$, the conditions implying the existence of the (scalar valued) stochastic integral $H.M$ are less restrictive than the existence of the ``componentwise'' stochastic integral, unless the components of $M$ are orthogonal (this result was due to Galtchouk, 1975). The theory of vector stochastic integrals, though parallel to the scalar theory, requires a careful theory given in this paper

Comment: Another approach, yielding an equivalent definition, is followed by L. Schwartz in his article 1530 on formal semimartingales

Keywords: Semimartingales, Stochastic integrals

Nature: Original

Retrieve article from Numdam

Intégrales stochastiques par rapport à une semi-martingale vectorielle et changements de filtration (Stochastic calculus, General theory of processes)

Given a square integrable vector martingale $M$ and a previsible vector process $H$, the conditions implying the existence of the (scalar valued) stochastic integral $H.M$ are less restrictive than the existence of the ``componentwise'' stochastic integral, unless the components of $M$ are orthogonal (this result was due to Galtchouk, 1975). The theory of vector stochastic integrals, though parallel to the scalar theory, requires a careful theory given in this paper

Comment: Another approach, yielding an equivalent definition, is followed by L. Schwartz in his article 1530 on formal semimartingales

Keywords: Semimartingales, Stochastic integrals

Nature: Original

Retrieve article from Numdam