Existencia de soluciones de ecuaciones diferenciales estocásticas
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Ecuaciones, diferenciales estocásticas (es)Descargas
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 < ∞, 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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Derechos de autor 1985 Revista Colombiana de Matemáticas

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.