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PhD dissertation PDF

 

1. Potential theory for systems of nonlinear SPDES:

 

  1. Dalang, R.C. and Nualart, E. (2004), Potential theory for hyperbolic SPDEs, The Annals of Probability,  32, 2009-2148  PDF 
  2. Dalang, R.C., Khoshnevisan, D., and Nualart, E. (2007), Hitting probabilites for systems of nonlinear stochastic heat equations with additive noise, ALEA, 3, 231-271  PDF 
  3. Dalang, R.C., Khoshnevisan, D., and Nualart, E. (2009), Hitting probabilities for systems of nonlinear heat equations with multiplicative noise, Probability Theory and Related Fields, 144, 371-427  PDF 
  4. Dalang, R.C., Khoshnevisan, D., and Nualart, E. (2009), Hitting probabilities for systems of nonlinear spatially homogeneous stochastic heat equations, In preparation 



2. Potential theory for systems of linear SPDEs:

 

  1. Khoshnevisan, D. and Nualart, E. (2008), Level sets of the stochastic wave equation driven by a symmetric Lévy noise, Bernouilli, 14, 899-925  PDF 
  2. Nualart, E. and Viens, F. (2009), The fractional stochastic heat equation on the circle: Time regularity and potential theory, Stochastic Processes and Their Applications, 119, 1505-1540  PDF  
  3. Foondun, M., Khoshnevisan, D., and Nualart, E. (2009), A local-time correspondence for stochastic partial differential equations, To appear in Transactions of the American Mathematical Society PDF



3. Potential theory for multiparameter processes:

 

  1.  Mountford, T.S. and Nualart, E. (2004), Level Sets of Multiparameter Brownian Motions, Electronic Journal of Probability, 9, 594-614  PDF
  2. Dalang, R.C., Khoshnevisan, d., Nualart, E., Xiao, Y., and Wu, D. (2009), Critical Brownian sheet does not have double points, Preprint  PDF 



4. Lower bounds for densities:

 

  1. Nualart, E. (2004), Exponential divergence estimates and heat kernel tail, C. R. Math. Acad. Sci. Paris, 338, 77-80  PDF
  2. Malliavin, P. and Nualart, E. (2009), Density minoration of a strongly non-degenrated random variable, Journal of Functional Analysis, 256, 4197-4214  PDF 
  3. Guérin, H, Méléard, S., and Nualart, E. (2006), Estimates for the density of a nonlinear Landau process, Journal of Functional Analysis, 238, 649-677  PDF 
  4. Nualart, E. (2009), Strict positivity of the density for nonlinear spatially homogeneous SPDEs, Submitted for publication  PDF