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Stochastic Measure Diffusion Processes

Published online by Cambridge University Press:  20 November 2018

Donald A. Dawson
Donald A. Dawson*
Affiliation:
Department of Mathematics, Carleton University OttawaOnt. K1S 5B6
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The purpose of this article is to give an introduction to the study of a class of stochastic partial differential equations and to give a brief review of some of the recent developments in this field. This study has evolved naturally out of the theory of stochastic differential equations initiated in a pioneering paper of K. Itô [13]. In order to set this review in its appropriate setting we begin by considering a simple scalar stochastic differential equation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 2 , 01 June 1979 , pp. 129 - 138
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Bose, A., Brownian measure processes. Ph.D. Thesis, Carleton University, 1977.Google Scholar
2. Chow, P. L., Stochastic partial equations in turbulence related problems. In Probabilistic Analysis and Related Topics, Vol. 1, Academic Press, 1978.Google Scholar
3. Dawson, D. A., Generalized stochastic integrals and equations. Trans. Amer. Math. Soc. 147 (1970),473-506 Google Scholar
4. Dawson, D. A., Stochastic evolution equations and related measure processes, J. Mult. Anal. 5 (1975),1-52.Google Scholar
5. Dawson, D. A., The critical measure diffusion. Zeit. Wahr. verw Geb. 40 (1977),125-145.Google Scholar
6. Dawson, D. A., Limit theorems for interaction free geostochastic systems. To appear in Sena Colloquia Mathematica Societatis Janos Bolyai.Google Scholar
7. Dawson, D. A., Geostochastic calculus. Can. J. Stat., 6 (1979),143-168.Google Scholar
8. Dawson, D. A., An infinite geostochastic system. To appear in Multivariate Analysis 5, North Holland.Google Scholar
9. Dawson, D. A. and Hochberg, K. J., The carrying dimension of a stochastic measure diffusion, Ann. Prob., to appear.Google Scholar
10. Feller, W., Diffusion processes in genetics. In Proc. Second Berkeley Symp., Univ. of Calif. Press, 1951,227-246.Google Scholar
11. Fleming, W. and Viot, M., Some measure-valued population processes. Proc. Intl. Conf. Stoch. Anal., Northwestern Univ., Academic Press, 1978.Google Scholar
12. Holley, R. A. and Stroock, D. W., Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motion, to appear.Google Scholar
13. Itô, K., On stochastic differential equations. Mem. Amer. Math. Soc. No. 4, 1951.Google Scholar
14. McKean, H. P., Stochastic integrals. Academic Press, 1969.Google Scholar
15. Mizuno, S., On some infinite dimensional martingale problems and related stochastic evolution equations. Ph.D. thesis, Carleton University, 1978.Google Scholar
16. Papanicolaou, G. C., Asymptotic analysis of transport processes. Bull. Amer. Math. Soc. 81 (1975),330-392.Google Scholar
17. Stroock, D. W. and Varadhan, S. R. S., Diffusion processes with continuous coefficients, I, II. Comm. Pure Appl. Math. 22 (1969),345-400,479-530.Google Scholar
18. Viot, M., Méthodes de compacité et de monotonie compacité pour les équations aux dérivées partielles stochastiques. Thèse, Univ. de Paris, 1975.Google Scholar