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References
- Carmona, René A.; Viens, Frederi G. Almost-sure exponential behavior of a stochastic Anderson model with continuous space parameter. Stochastics Stochastics Rep. 62 (1998), no. 3-4, 251--273. MR1615092 (99c:60126)
- Crisan, Dan. Superprocesses in a Brownian environment.Stochastic analysis with applications to mathematical finance. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004), no. 2041, 243--270. MR2052263 (2005h:60306)
- D. Crisan and J. Xiong (2006). A central limit type theorem forparticle filter. To appear in Comm. Stoch. Anal.
- Dawson, D. A. The critical measure diffusion process. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 40 (1977), no. 2, 125--145. MR0478374 (57 #17857)
- Dawson, D. A.; Iscoe, I.; Perkins, E. A. Super-Brownian motion: path properties and hitting probabilities. Probab. Theory Related Fields 83 (1989), no. 1-2, 135--205. MR1012498 (90k:60073)
- Dawson, Donald A.; Salehi, Habib. Spatially homogeneous random evolutions. J. Multivariate Anal. 10 (1980), no. 2, 141--180. MR0575923 (82c:60102)
- S.N. Ethier and T.G. Kurtz (1986). Markov Processes: Characterization and Convergence. Wiley.
- Florescu, Ionut; Viens, Frederi. Sharp estimation of the almost-sure Lyapunov exponent for the Anderson model in continuous space. Probab. Theory Related Fields 135 (2006), no. 4, 603--644. MR2240702
- A. Friedman (1975). Stochastic Differential Equations and Applications, Vol. 1, Academic Press.
- Iscoe, I. A weighted occupation time for a class of measure-valued branching processes. Probab. Theory Relat. Fields 71 (1986), no. 1, 85--116. MR0814663 (87c:60070)
- Iscoe, I. On the supports of measure-valued critical branching Brownian motion. Ann. Probab. 16 (1988), no. 1, 200--221. MR0920265 (88j:60097)
- Kallenberg, Olav. Foundations of modern probability.Second edition.Probability and its Applications (New York). Springer-Verlag, New York, 2002. xx+638 pp. ISBN: 0-387-95313-2 MR1876169 (2002m:60002)
- Kallianpur, Gopinath. Stochastic filtering theory. Applications of Mathematics, 13. Springer-Verlag, New York-Berlin, 1980. xvi+316 pp. ISBN: 0-387-90445-X MR0583435 (82f:60089)
- G. Kallianpur and J. Xiong (1995). Stochastic Differential Equations in Infinite Dimensional Spaces. IMS Lecture Notes -Monograph Series 26.
- Kotelenez, Peter. Comparison methods for a class of function valued stochastic partial differential equations. Probab. Theory Related Fields 93 (1992), no. 1, 1--19. MR1172936 (93i:60116)
- Kunita, Hiroshi. Stochastic flows and stochastic differential equations.Cambridge Studies in Advanced Mathematics, 24. Cambridge University Press, Cambridge, 1990. xiv+346 pp. ISBN: 0-521-35050-6 MR1070361 (91m:60107)
- Kurtz, Thomas G.; Xiong, Jie. Particle representations for a class of nonlinear SPDEs. Stochastic Process. Appl. 83 (1999), no. 1, 103--126. MR1705602 (2000g:60108)
- Li, Zenghu; Wang, Hao; Xiong, Jie. Conditional log-Laplace functionals of immigration superprocesses with dependent spatial motion. Acta Appl. Math. 88 (2005), no. 2, 143--175. MR2169037 (2006h:60138)
- Mueller, Carl; Tribe, Roger. A singular parabolic Anderson model. Electron. J. Probab. 9 (2004), no. 5, 98--144 (electronic). MR2041830 (2005b:60157)
- Mytnik, Leonid. Superprocesses in random environments. Ann. Probab. 24 (1996), no. 4, 1953--1978. MR1415235 (97h:60046)
- E. Perkins (2002).Dawson-Watanabe Superprocesses and Measure-valued Diffusions, in Ecole d'Età de ProbabilitÃs de Saint Flour 1999, Lect.Notes. in Math. 1781, Springer-Verlag.
- Tindel, Samy; Viens, Frederi. Relating the almost-sure Lyapunov exponent of a parabolic SPDE and its coefficients' spatial regularity. Potential Anal. 22 (2005), no. 2, 101--125. MR2137056 (2006j:60067)
- Xiong, Jie. A stochastic log-Laplace equation. Ann. Probab. 32 (2004), no. 3B, 2362--2388. MR2078543 (2005e:60137)
- Xiong, Jie. Long-term behavior for superprocesses over a stochastic flow. Electron. Comm. Probab. 9 (2004), 36--52 (electronic). MR2081458 (2005k:60155)
- J. Xiong (2006). An Introduction to Stochastic Filtering Theory. To be published by Oxford University Press.

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