# Probability density for a hyperbolic SPDE with time dependent coefficients

Marta Sanz-Solé; Iván Torrecilla-Tarantino

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 365-380
- ISSN: 1292-8100

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topSanz-Solé, Marta, and Torrecilla-Tarantino, Iván. "Probability density for a hyperbolic SPDE with time dependent coefficients." ESAIM: Probability and Statistics 11 (2007): 365-380. <http://eudml.org/doc/250103>.

@article{Sanz2007,

abstract = {
We prove the existence and smoothness of density for the solution
of a hyperbolic SPDE with free term coefficients depending on
time, under hypoelliptic non degeneracy conditions. The result
extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional
setting.
},

author = {Sanz-Solé, Marta, Torrecilla-Tarantino, Iván},

journal = {ESAIM: Probability and Statistics},

keywords = {Malliavin calculus. Stochastic partial differential
equations. Two-parameter processes.; Malliavin calculus; stochastic partial differential equations; two-parameter processes},

language = {eng},

month = {8},

pages = {365-380},

publisher = {EDP Sciences},

title = {Probability density for a hyperbolic SPDE with time dependent coefficients},

url = {http://eudml.org/doc/250103},

volume = {11},

year = {2007},

}

TY - JOUR

AU - Sanz-Solé, Marta

AU - Torrecilla-Tarantino, Iván

TI - Probability density for a hyperbolic SPDE with time dependent coefficients

JO - ESAIM: Probability and Statistics

DA - 2007/8//

PB - EDP Sciences

VL - 11

SP - 365

EP - 380

AB -
We prove the existence and smoothness of density for the solution
of a hyperbolic SPDE with free term coefficients depending on
time, under hypoelliptic non degeneracy conditions. The result
extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional
setting.

LA - eng

KW - Malliavin calculus. Stochastic partial differential
equations. Two-parameter processes.; Malliavin calculus; stochastic partial differential equations; two-parameter processes

UR - http://eudml.org/doc/250103

ER -

## References

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- P. Cattiaux and L. Mesnager, Hypoelliptic non-homogeneous diffusions. PTRF123 (2002) 453–483. Zbl1009.60058
- M. Chen and X. Zhou, Applications of Malliavin calculus to stochastic differential equations with time-dependent coefficients. Acta Appli. Math. Sinica7 (1991) 193–216. Zbl0751.60048
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- P. Malliavin, Stochastic calculus of variations and hypoelliptic operators, in Proc. Inter. Symp. on Stoch. Diff. Equations, Kyoto 1976, Tokyo and Wiley, New York (1978) 195–263.
- J.R. Norris, Simplified Malliavin calculus, in Séminaire de Probabilités XX.LNM1204 (1986) 101–130. Zbl0609.60066
- D. Nualart, The Malliavin Calculus and Related Topics. Probability and its Applications. Springer-Verlag, 2nd Edition (2006). Zbl1099.60003
- D. Nualart and M. Sanz, Malliavin calculus for two-parameter Wiener functionals. Z. für Wahrscheinlichkeitstheorie verw.Gebiete70 (1985) 573–590. Zbl0595.60065
- P.E. Protter, Stochastic Integration and Differential Equations. Applications of Mathematics. Stochastic Modelling and Applied Probability. Springer, 2nd Edition 21 (2004). Zbl1041.60005
- D.W. Stroock, Some applications of stochastic calculus to partial differential equations, in École d'Été de Probabilités de Saint Flour. LNM976 (1983) 267–382.
- S. Taniguchi, Applications of Malliavin's calculus to time-dependent systems of heat equations. Osaka J. Math.22 (1985) 307–320. Zbl0583.35055

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