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References

  • Stochastic modelling in physical oceanography. Edited by Robert J. Adler, Peter Müller and Boris Rozovskiĭ. Progress in Probability, 39. Birkhäuser Boston, Inc., Boston, MA, 1996. xii+467 pp. ISBN: 0-8176-3798-2 MR1383868
  • Bally, V.; Gyöngy, I.; Pardoux, É. White noise driven parabolic SPDEs with measurable drift. J. Funct. Anal. 120 (1994), no. 2, 484--510. MR1266318
  • Bally, Vlad; Millet, Annie; Sanz-Solé, Marta. Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations. Ann. Probab. 23 (1995), no. 1, 178--222. MR1330767
  • Bardina, Xavier; Florit, Carme. Approximation in law to the $d$-parameter fractional Brownian sheet based on the functional invariance principle. Rev. Mat. Iberoamericana 21 (2005), no. 3, 1037--1052. MR2232675
  • Bardina, Xavier; Jolis, Maria. Weak approximation of the Brownian sheet from a Poisson process in the plane. Bernoulli 6 (2000), no. 4, 653--665. MR1777689
  • Bardina, Xavier; Jolis, Maria; Tudor, Ciprian A. Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes. Statist. Probab. Lett. 65 (2003), no. 4, 317--329. MR2039877
  • Björk, Tomas. A geometric view of interest rate theory. Option pricing, interest rates and risk management, 241--277, Handb. Math. Finance, Cambridge Univ. Press, Cambridge, 2001. MR1848554
  • Carmona, René A.; Fouque, Jean-Pierre. A diffusion approximation result for two parameter processes. Probab. Theory Related Fields 98 (1994), no. 3, 277--298. MR1262967
  • Carmona, René; Nualart, David. Random nonlinear wave equations: smoothness of the solutions. Probab. Theory Related Fields 79 (1988), no. 4, 469--508. MR0966173
  • Čencov, N. N. Limit theorems for certain classes of random functions. (Russian) 1960 Proc. All-Union Conf. Theory Prob. and Math. Statist. (Erevan, 1958) (Russian) pp. 280--285 Izdat. Akad. Nauk Armjan. SSR, Erevan MR0195132
  • Conus, Daniel; Dalang, Robert C. The non-linear stochastic wave equation in high dimensions. Electron. J. Probab. 13 (2008), no. 22, 629--670. MR2399293
  • Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136
  • Dalang, Robert C. Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s. Electron. J. Probab. 4 (1999), no. 6, 29 pp. (electronic). MR1684157
  • Dawson, Donald A.; Salehi, Habib. Spatially homogeneous random evolutions. J. Multivariate Anal. 10 (1980), no. 2, 141--180. MR0575923
  • Debussche, Arnaud. Weak approximation of stochastic partial differential equations: the nonlinear case. Math. Comp. 80 (2011), no. 273, 89--117. MR2728973
  • Debussche, Arnaud; Printems, Jacques. Weak order for the discretization of the stochastic heat equation. Math. Comp. 78 (2009), no. 266, 845--863. MR2476562
  • Florit, Carme; Nualart, David. Diffusion approximation for hyperbolic stochastic differential equations. Stochastic Process. Appl. 65 (1996), no. 1, 1--15. MR1422876
  • Fournier, Nicolas. Malliavin calculus for parabolic SPDEs with jumps. Stochastic Process. Appl. 87 (2000), no. 1, 115--147. MR1751168
  • Gubinelli, Massimiliano; Lejay, Antoine; Tindel, Samy. Young integrals and SPDEs. Potential Anal. 25 (2006), no. 4, 307--326. MR2255351
  • Hausenblas, Erika. Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure. Electron. J. Probab. 10 (2005), 1496--1546. MR2191637
  • Imkeller, Peter. Energy balance models—viewed from stochastic dynamics. Stochastic climate models (Chorin, 1999), 213--240, Progr. Probab., 49, Birkhäuser, Basel, 2001. MR1948298
  • Kac, Mark. A stochastic model related to the telegrapher's equation. Reprinting of an article published in 1956. Papers arising from a Conference on Stochastic Differential Equations (Univ. Alberta, Edmonton, Alta., 1972). Rocky Mountain J. Math. 4 (1974), 497--509. MR0510166
  • León, Jorge A.; Sarrà, Mònica. A non-homogeneous wave equation driven by a Poisson process. Stochastic models (Mexico City, 2002), 203--211, Contemp. Math., 336, Amer. Math. Soc., Providence, RI, 2003. MR2037166
  • Manthey, Ralf. Weak convergence of solutions of the heat equation with Gaussian noise. Math. Nachr. 123 (1985), 157--168. MR0809342
  • Manthey, Ralf. Weak approximation of a nonlinear stochastic partial differential equation. Random partial differential equations (Oberwolfach, 1989), 139--148, Internat. Ser. Numer. Math., 102, Birkhäuser, Basel, 1991. MR1185745
  • Maslowski, Bohdan; Nualart, David. Evolution equations driven by a fractional Brownian motion. J. Funct. Anal. 202 (2003), no. 1, 277--305. MR1994773
  • Millet, Annie; Sanz-Solé, Marta. A stochastic wave equation in two space dimension: smoothness of the law. Ann. Probab. 27 (1999), no. 2, 803--844. MR1698971
  • Mueller, Carl; Mytnik, Leonid; Stan, Aurel. The heat equation with time-independent multiplicative stable Lévy noise. Stochastic Process. Appl. 116 (2006), no. 1, 70--100. MR2186840
  • Quer-Sardanyons, Lluís; Tindel, Samy. The 1-d stochastic wave equation driven by a fractional Brownian sheet. Stochastic Process. Appl. 117 (2007), no. 10, 1448--1472. MR2353035
  • Saint Loubert Bié, Erwan. Étude d'une EDPS conduite par un bruit poissonnien. (French) [Study of an SPDE driven by a Poisson noise] Probab. Theory Related Fields 111 (1998), no. 2, 287--321. MR1633586
  • Stroock, Daniel W. Lectures on topics in stochastic differential equations. With notes by Satyajit Karmakar. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 68. Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin-New York, 1982. iii+93 pp. ISBN: 3-540-11549-8 MR0685758
  • Tindel, Samy. Diffusion approximation for elliptic stochastic differential equations. Stochastic analysis and related topics, V (Silivri, 1994), 255--268, Progr. Probab., 38, Birkhäuser Boston, Boston, MA, 1996. MR1396335
  • Tindel, S.; Tudor, C. A.; Viens, F. Stochastic evolution equations with fractional Brownian motion. Probab. Theory Related Fields 127 (2003), no. 2, 186--204. MR2013981
  • Tessitore, Gianmario; Zabczyk, Jerzy. Wong-Zakai approximations of stochastic evolution equations. J. Evol. Equ. 6 (2006), no. 4, 621--655. MR2267702
  • Walsh, John B. A stochastic model of neural response. Adv. in Appl. Probab. 13 (1981), no. 2, 231--281. MR0612203
  • Walsh, John B. An introduction to stochastic partial differential equations. École d'été de probabilités de Saint-Flour, XIV—1984, 265--439, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876085
  • Wichura, Michael J. Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters. Ann. Math. Statist. 40 1969 681--687. MR0246359
  • Yor, Marc. Le drap brownien comme limite en loi de temps locaux linéaires. (French) [The Brownian sheet as a limit in law of linear local times] Seminar on probability, XVII, 89--105, Lecture Notes in Math., 986, Springer, Berlin, 1983. MR0770400


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