Strong solution of Itô type set-valued stochastic differential equation

Jun Gang Li; Shou Mei Li; Ogura, Yukio
September 2010
Acta Mathematica Sinica;Sep2010, Vol. 26 Issue 9, p1739
Academic Journal
In this paper, we shall firstly illustrate why we should introduce an Itô 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 Itô type set-valued stochastic differential equation.


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