Existencia de soluciones de ecuaciones diferenciales estocásticas
In classic theorems, when we have a stochastic differential equation of the form dXt = f(t,Xt)dt + G(t,Xt)dWt, Xt = ξ, to ≤ t ≤ T and lt; ∞, where Wt is a Wiener Process and ξ is a random variable independent of Wt-Wto for t ≥ to in order to have existence and uniqueness of solutions it is suppose...
- Autores:
-
Muñoz de Ozak, Myriam
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1985
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/48811
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/48811
http://bdigital.unal.edu.co/42268/
- Palabra clave:
- Ecuaciones
diferenciales estocásticas
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In classic theorems, when we have a stochastic differential equation of the form dXt = f(t,Xt)dt + G(t,Xt)dWt, Xt = ξ, to ≤ t ≤ T and lt; ∞, where Wt is a Wiener Process and ξ is a random variable independent of Wt-Wto for t ≥ to in order to have existence and uniqueness of solutions it is supposed the existence of a constant K such that: (Lipschitz condition) for all t ϵ [to,T], x,y ∈Rd, |f(t,x)-f(t,y)| + |G(t,x)-G(t,y)| ≤ K|x-y|· And for all t ∈|to,T | and x ∈ Rd, |f(t,x)|2+|G(t,x)|2≤ K2(1+|x|2). In this article we prove an existence theorem under weaker hypothesis: we require only that f and G be continuous in the second variable and the existence of a function m ϵ L2 [to,T] such that |f(t,x)|+|G(t,x)| ≤ m(t) for alI t ∈ [to,T] and x ∈ Rd. |
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