A PDE approach to stochastic invariance

Hitoshi Ishii; Paola Loreti; Maria Elisabetta Tessitore

doi:10.3934/dcds.2000.6.651

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2000, Volume 6, Issue 3: 651-664. Doi: 10.3934/dcds.2000.6.651

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A PDE approach to stochastic invariance

1.
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397
2.
Dipartimento Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza", Via A. Scarpa, 16, 00161 Roma
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

Received: October 31, 1999

Revised: December 31, 1999

Published: June 2000

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Stochastic differential equations,
second-order Hamilton-Jacobi-Bellman equation,
viscosity solutions,
invariance property.

Mathematics Subject Classification: 60H10, 49L20, 49L25, 35J70.

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