Abstract
In this paper, the regularity and the ψ-semigroup property of the solutions to a class of stochastic partial differential equations (SPDEs) derived from a class of interacting superprocesses are investigated.
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DA PRATO G. AND ZABCZYK J. (1992). Stochastic Equations in Infinite Dimensions. Cambridge University Press, 1992.
DAWSON D.A., LI Z., AND WANG H. (2001). Superprocesses with dependent spatial motion AND general branching densities. Electron. J. Probab., V6, 25: 1–33, 200l.
KURTZ T.G. AND XIONG J. (1999). Particle representations for a class of nonlinear SPDEs. Stoch. Proc. Appl., 83: 103–126, 1999.
LI Z.H., WANG H., AND XIONG J. (2004). Conditional Log-Laplace functionals of immigration superprocesses with dependent spatial motion. Submitted, 2004. (Available at http://darkwing.uoregon.edu/~haowang/research/pub.html.)
ROZOVSKII B.L. (1990). Stochastic Evolution Systems — Linear Theory AND Applications to Non-linear Filtering. Kluwer Academic Publishers, 1990.
WALSH J.B. (1986). An introduction to stochast ic partial differential equations. Lecture Notes in Math., 1180: 265–439, 1986.
WANG H. (1998). A class of measure-valued branching diffusions in a rANDom medium. Sto chastic Anal. Appl., 16(4): 753–786, 1998.
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Wang, H. (2005). Existence and Uniqueness of Classical, Nonnegative, Smooth Solutions of a Class of Semi-Linear Spdes. In: Waymire, E.C., Duan, J. (eds) Probability and Partial Differential Equations in Modern Applied Mathematics. The IMA Volumes in Mathematics and its Applications, vol 140. Springer, New York, NY. https://doi.org/10.1007/978-0-387-29371-4_15
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DOI: https://doi.org/10.1007/978-0-387-29371-4_15
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