Advances in Differential Equations
- Adv. Differential Equations
- Volume 7, Number 9 (2002), 1045-1072.
Viability of moving sets for stochastic differential equation
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.
Adv. Differential Equations Volume 7, Number 9 (2002), 1045-1072.
First available in Project Euclid: 29 April 2013
Permanent link to this document
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. https://projecteuclid.org/euclid.ade/1367241459.