SPDEs with pseudodifferential generators: the existence of a density

Samy Tindel

Applicationes Mathematicae (2000)

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

Abstract

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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 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 ) ∈ [ 0 , T ] × 𝒪 is absolutely continuous with respect to the Lebesgue measure.

How to cite

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Tindel, 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 -

References

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