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Current position:
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Teaching 2009-2010:
- Probability
theory (Degree in Statistics).
- Inferential
Statistics (Degree in Business Administration - Law).
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Research:
- Stochastic
analysis and Malliavin calculus.
- Stochastic
partial differential equations: existence and uniqueness of solutions,
path properties, existence and smoothness of the density, Gaussian
estimates for the density.
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Publications:
- Existence
of density for the solution to the three-dimensional stochastic wave
equation (with Marta Sanz-Solé), RACSAM Revista de la Real
Academia de Ciencias Exactas,
Físicas y Naturales Serie A Mat.
97 (2003), no. 1, 63-68.
- Absolute continuity of
the law of the solution to the 3-dimensional stochastic wave
equation (with Marta Sanz-Solé), Journal
of Functional Analysis 206 (2004), no. 1, 1-32.
- A stochastic wave
equation
in dimension 3: smoothness of the law (with Marta
Sanz-Solé),
Bernoulli 10 (2004), no. 1, 165-186.
- Space
semi-discretisations
for a stochastic wave equation (with Marta Sanz-Solé),
Potential Analysis 24 (2006), no. 4, 303-332.
- The
1-d stochastic wave equation driven by a fractional Brownian sheet
(with
Samy Tindel), Stochastic Processes and their Applications 117
(2007), 1448-1472.
- Existence
and smoothness of the density for spatially homogeneous SPDEs (with
David Nualart), Potential Analysis 27 (2007), 281-299.
- Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations (with
David Nualart), Stochastic Processes and their Applications 119 (2009), 3914-3938.
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Preprints:
- Weak convergence for the stochastic heat equation driven by Gaussian white noise (with Xavier Bardina and Maria Jolis),
arXiv:0907.2508v1
- Optimal Gaussian density estimates for a class of stochastic equations with additive noise (with
David Nualart),
arXiv:0912.3707v1
- Stochastic integrals for spde's: a comparison (with Robert C. Dalang),
arXiv:1001.0856v1
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Work in progress:
- Pathwise definition of elliptic SPDEs in dimension 1 (with Samy Tindel).
- Existence of weak solutions for a class of semilinear stochastic wave equations (with Carlo Marinelli).
- Gaussian density estimates for spatially homogeneous SPDEs with multiplicative noise (with Eulàlia Nualart).
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Some presentations in seminars and conferences:
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Curriculum |
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Barcelona Probability Seminar | |
