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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Abstract

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

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

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1367241459

Mathematical Reviews number (MathSciNet)
MR1920372

Zentralblatt MATH identifier
1037.60055

Subjects
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

Citation

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.


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