Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
Existence and uniqueness of solutions of stochastic functional differential equations
-
Max-K. von Renesse
Veröffentlicht/Copyright:
9. September 2010
Abstract
Using a variant of the Euler–Maruyama scheme for stochastic functional differential equations with bounded memory driven by Brownian motion we show that only weak one-sided local Lipschitz (or “monotonicity”) conditions are sufficient for local existence and uniqueness of strong solutions. In case of explosion the method yields the maximal solution up to the explosion time. We also provide a weak growth condition which prevents explosions to occur. In an appendix we formulate and prove four lemmas which may be of independent interest: three of them can be viewed as rather general stochastic versions of Gronwall's Lemma, the final one provides tail bounds for Hölder norms of stochastic integrals.
Keywords.: Stochastic functional differential equation; existence of solution; maximal solution; uniqueness of solution; Dereich lemma; stochastic Gronwall lemma
Received: 2009-06-01
Accepted: 2009-11-04
Published Online: 2010-09-09
Published in Print: 2010-September
© de Gruyter 2010
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- Existence and optimality conditions in stochastic control of linear BSDEs
- On random equations and applications to random fixed point theorems
- Minimum distance parameter estimation for a stochastic equation with additive fractional Brownian sheet
- Homogenization of reflected semilinear PDEs with nonlinear Neumann boundary condition
- Optimality conditions of controlled backward doubly stochastic differential equations
- Existence and uniqueness of solutions of stochastic functional differential equations
Schlagwörter für diesen Artikel
Stochastic functional differential equation;
existence of solution;
maximal solution;
uniqueness of solution;
Dereich lemma;
stochastic Gronwall lemma
Artikel in diesem Heft
- Existence and optimality conditions in stochastic control of linear BSDEs
- On random equations and applications to random fixed point theorems
- Minimum distance parameter estimation for a stochastic equation with additive fractional Brownian sheet
- Homogenization of reflected semilinear PDEs with nonlinear Neumann boundary condition
- Optimality conditions of controlled backward doubly stochastic differential equations
- Existence and uniqueness of solutions of stochastic functional differential equations
