July  2000, 6(3): 651-664. doi: 10.3934/dcds.2000.6.651

A PDE approach to stochastic invariance

1. 

Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan

2. 

Dipartimento Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza", Via A. Scarpa, 16, 00161 Roma, Italy

3. 

Dipartimento di Studi Economico - Finanziari e Metodi Quantitativi (S.E.F.E ME.Q.), Università di Roma "Tor Vergata", Via di Tor Vergata s.n.c., 00133 Roma, Italy

Received  November 1999 Revised  January 2000 Published  April 2000

We study an invariance property for a controlled stochastic differential equation and give a few of its characterizations in connection with the corresponding Hamilton-Jacobi-Bellman equation.
Citation: Hitoshi Ishii, Paola Loreti, Maria Elisabetta Tessitore. A PDE approach to stochastic invariance. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 651-664. doi: 10.3934/dcds.2000.6.651
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