TITLE

# Strong solution of ItÃ´ type set-valued stochastic differential equation

AUTHOR(S)
Jun Gang Li; Shou Mei Li; Ogura, Yukio
PUB. DATE
September 2010
SOURCE
Acta Mathematica Sinica;Sep2010, Vol. 26 Issue 9, p1739
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In this paper, we shall firstly illustrate why we should introduce an ItÃ´ type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the ItÃ´ type set-valued stochastic differential equation.
ACCESSION #
52837148

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