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References

  • Adams, Robert A.; Fournier, John J. F. Sobolev spaces. Second edition. Pure and Applied Mathematics (Amsterdam), 140. Elsevier/Academic Press, Amsterdam, 2003. xiv+305 pp. ISBN: 0-12-044143-8 MR2424078
  • 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
  • Jacod, Jean. Weak and strong solutions of stochastic differential equations. Stochastics 3, no. 3, 171--191. (1980), MR0573202
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • Konno, N.; Shiga, T. Stochastic partial differential equations for some measure-valued diffusions. Probab. Theory Related Fields 79 (1988), no. 2, 201--225. MR0958288
  • Kurtz, Thomas G. The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities. Electron. J. Probab. 12 (2007), 951--965. MR2336594
  • Meyer, Paul-A. Probability and potentials. Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London 1966 xiii+266 pp. MR0205288
  • Carl Mueller, Leonid Mytnik, and Edwin Perkins, Nonuniqueness for a parabolic SPDE with 3/4 - ε-Hölder diffusion coefficients, preprint (2012), arXiv:1201.2767v1 [math.PR].
  • Mytnik, Leonid. Superprocesses in random environments. Ann. Probab. 24 (1996), no. 4, 1953--1978. MR1415235
  • Mytnik, Leonid; Perkins, Edwin. Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case. Probab. Theory Related Fields 149 (2011), no. 1-2, 1--96. MR2773025
  • Mytnik, Leonid; Perkins, Edwin; Sturm, Anja. On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients. Ann. Probab. 34 (2006), no. 5, 1910--1959. MR2271487
  • Perkins, Edwin. Dawson-Watanabe superprocesses and measure-valued diffusions. Lectures on probability theory and statistics (Saint-Flour, 1999), 125--324, Lecture Notes in Math., 1781, Springer, Berlin, 2002. MR1915445
  • Peszat, Szymon; Zabczyk, Jerzy. Nonlinear stochastic wave and heat equations. Probab. Theory Related Fields 116 (2000), no. 3, 421--443. MR1749283
  • Reimers, Mark. One-dimensional stochastic partial differential equations and the branching measure diffusion. Probab. Theory Related Fields 81 (1989), no. 3, 319--340. MR0983088
  • Rippl, Thomas. Pathwise uniqueness of the stochastic heat equation with Hölder continuous diffusion coefficient and colored noise, rlhttp://hdl.handle.net/11858/00-1735-0000-000D-F0ED-A, 2012.
  • Sanz-Solé, M.; Sarrà, M. Hölder continuity for the stochastic heat equation with spatially correlated noise. Seminar on Stochastic Analysis, Random Fields and Applications, III (Ascona, 1999), 259--268, Progr. Probab., 52, Birkhäuser, Basel, 2002. MR1958822
  • Sturm, Anja. On convergence of population processes in random environments to the stochastic heat equation with colored noise. Electron. J. Probab. 8 (2003), no. 6, 39 pp. (electronic). MR1986838
  • 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
  • Xiong, Jie. Super-Brownian motion as the unique strong solution to an SPDE, Ann. Probab. 41 (2013), no. 2, 1030--1054.
  • Yamada, Toshio; Watanabe, Shinzo. On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 1971 155--167. MR0278420
  • Zähle, Henryk. Approximation of SDEs by population-size-dependent Galton-Watson processes. Stoch. Anal. Appl. 28 (2010), no. 2, 377--388. MR2739564


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