Advances in Differential Equations

Viability of moving sets for stochastic differential equation

Rainer Buckdahn, Marc Quincampoix, Catherine Rainer, and Aurel Răşcanu

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We study the existence of solutions of stochastic differential equations with a state constraint depending on the time. We provide a necessary and sufficient characterization of closed, time depending constraints for which there exists a solution of a given stochastic differential equation. This characterization is given in terms of viscosity super- and subsolution of some suitable partial differentiable equations. The above property, called viability, is stated for both forward and backward stochastic differential equations.

Article information

Adv. Differential Equations, Volume 7, Number 9 (2002), 1045-1072.

First available in Project Euclid: 29 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J53: Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.) 93E20: Optimal stochastic control


Buckdahn, Rainer; Quincampoix, Marc; Rainer, Catherine; Răşcanu, Aurel. Viability of moving sets for stochastic differential equation. Adv. Differential Equations 7 (2002), no. 9, 1045--1072.

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