# SPDEs with pseudodifferential generators: the existence of a density

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 3, page 287-308
- ISSN: 1233-7234

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topTindel, Samy. "SPDEs with pseudodifferential generators: the existence of a density." Applicationes Mathematicae 27.3 (2000): 287-308. <http://eudml.org/doc/219274>.

@article{Tindel2000,

abstract = {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.},

author = {Tindel, Samy},

journal = {Applicationes Mathematicae},

keywords = {pseudodifferential operators; stochastic partial differential equations; Malliavin's calculus; Malliavin calculus},

language = {eng},

number = {3},

pages = {287-308},

title = {SPDEs with pseudodifferential generators: the existence of a density},

url = {http://eudml.org/doc/219274},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Tindel, Samy

TI - SPDEs with pseudodifferential generators: the existence of a density

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 3

SP - 287

EP - 308

AB - 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.

LA - eng

KW - pseudodifferential operators; stochastic partial differential equations; Malliavin's calculus; Malliavin calculus

UR - http://eudml.org/doc/219274

ER -

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