Higher-order stochastic partial differential equations with branching noises

Lijun Bo, Yongjin Wang, Liqing Yan

Front. Math. China ›› 2007, Vol. 3 ›› Issue (1) : 15-35.

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PDF(209 KB)
Front. Math. China ›› 2007, Vol. 3 ›› Issue (1) : 15-35. DOI: 10.1007/s11464-008-0006-0
Research Article

Higher-order stochastic partial differential equations with branching noises

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Abstract

In this paper, we propose a class of higher-order stochastic partial differential equations (SPDEs) with branching noises. The existence of weak (mild) solutions is established through weak convergence and tightness arguments.

Keywords

Higher-order stochastic partial differential equation (SPDE) / weak solution / tightness argument

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Lijun Bo, Yongjin Wang, Liqing Yan. Higher-order stochastic partial differential equations with branching noises. Front. Math. China, 2007, 3(1): 15‒35 https://doi.org/10.1007/s11464-008-0006-0

References

[1.]
Beghin L., Orsingher E., Ragozina T. Joint distributions of the maximum and the process for higher-order diffusions. Stoch Process Appl, 2001, 94: 71-93.
CrossRef Google scholar
[2.]
Bo L., Wang Y. Stochastic Cahn-Hilliard partial differential equations with Lévy spacetime white noises. Stoch Dyn, 2006, 6: 229-244.
CrossRef Google scholar
[3.]
Cardon-Weber C. Cahn-Hilliard stochastic equation: existence of the solution and of its density. Bernoulli, 2001, 7: 777-816.
CrossRef Google scholar
[4.]
Cardon-Weber C., Millet A. On strongly Petrovskiii’s parabolic SPDEs in arbitrary dimension and application to the stochastic Cahn-Hilliard equation. J Theor Probab, 2004, 17: 1-49.
CrossRef Google scholar
[5.]
Da Prato G., Debussche A. Stochastic Cahn-Hilliard equation. Nonlinear Anal, 1996, 26: 241-263.
CrossRef Google scholar
[6.]
Da Prato G., Zabczyk J. Ergodicity for Infinite Dimensional Systems, 1996, Cambridge: Cambridge Univ Press.
[7.]
Dalang R. Extending martingale measure stochastic integral with applications to spatially homogeneous SPDEs. Electron J Probab, 1999, 4: 1-29.
[8.]
Donati-Martin C., Pardoux E. White noise driven SPDEs with reflection. Probab Th Rel Fields, 1993, 95: 1-24.
CrossRef Google scholar
[9.]
Ethier S., Kurtz T. Markov Processes, Characterization and Convergence, 1986, New York: Wiley & Sons.
[10.]
Gyöngy I. Existence and uniqueness results for semilinear stochastic partial differential equations. Stoch Process Appl, 1998, 73: 271-299.
CrossRef Google scholar
[11.]
Hochberg J., Orsingher E. The arc-sine law and its analogs for processes governed by signed and complex measures. Stoch Process Appl, 1994, 52: 273-292.
CrossRef Google scholar
[12.]
Kolkovska E. On the Burgers equation with a stochastic stepping stone noisy term. J Math Sci, 2004, 121: 2645-2652.
CrossRef Google scholar
[13.]
Konno N., Shiga T. Stochastic partial differential equations for some measure-valued diffusions. Probab Th Rel Fields, 1988, 79: 201-225.
CrossRef Google scholar
[14.]
Lachal A. Distributions of sojourn time, maximum and minimum for pseudoprocesses governed by higher-order heat-type equations. Electron J Probab, 2003, 8: 1-53.
[15.]
Millet A., Morien P. On a nonlinear stochastic wave equation in the plane: existence and uniqueness of the solution. Ann Appl Probab, 2001, 11: 922-951.
CrossRef Google scholar
[16.]
Mueller C. Long-time existence for signed solution of the heat equation with a noise term. Probab Th Rel Fields, 1998, 110: 51-68.
CrossRef Google scholar
[17.]
Shiga T. Two contrasting properties of solutions for one-dimension stochastic partial differential equations. Can J Math, 1994, 46: 415-437.
[18.]
Walsh J. An Introduction to Stochastic Partial Differential Equations, 1986, Berlin: Springer-Verlag.
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