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SPDEs with pseudodifferential generators: the existence of a density

100%

Tindel S.

Applicationes Mathematicae

2000

tom 27

nr 3

287-308

We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain $\mathcal O$, and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point $(t,x)\in [0,T] \times \mathcal O$ is absolutely continuous with respect to the Lebesgue measure.

Asymptotic evaluation of the Poisson measures for tubes around jump curves

51%

Bardina X., Rovira C., Tindel S.

Applicationes Mathematicae

2002

tom 29

nr 2

145-156

We find the asymptotic behavior of P(||X-ϕ|| ≤ ε) when X is the solution of a linear stochastic differential equation driven by a Poisson process and ϕ the solution of a linear differential equation driven by a pure jump function.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Tindel S.

1 Bardina X.

1 Rovira C.

1 2002

1 2000

Wyniki wyszukiwania

SPDEs with pseudodifferential generators: the existence of a density

Asymptotic evaluation of the Poisson measures for tubes around jump curves