Any suggestions on a rigorous stochastic differential equations book?

Question

I have been looking through some books and they are not very rigorous. Any suggestions would be great.

Bjørn Kjos-Hanssen · Accepted Answer · 2014-01-15 03:45:38Z

4

Karatzas and Shreve Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics) (Volume 113) http://www.amazon.com/gp/aw/d/0387976558

answered Jan 15, 2014 at 3:45

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UwF · Accepted Answer · 2014-01-15 11:29:48Z

There are a lot of good books on the market, maybe you should describe more carefully what you want...

I think the following books don't lack rigor

C. Dellacherie and P.A. Meyer, Probabilités et Potentiel. Ch. I à IV. Hermann, Paris 1975, 290 pages
C. Dellacherie and P.A. Meyer, Probabilités et Potentiel. Ch. V à VIII, Hermann, Paris 1980, 476 pages
C. Dellacherie and P.A. Meyer, Probabilités et Potentiel. Ch IX à XI. Théorie discrète du potentiel. Hermann, Paris 1983, 229 pages
C. Dellacherie and P.A. Meyer, Probabilités et Potentiel. Ch. XII à XVI. Théorie du potentiel associée à une résolvante, théorie des processus de Markov Hermann, Paris 1987, 377 pages
C. Dellacherie, B. Maisonneuve and P.A. Meyer, Probabilités et Potentiel. Ch XVII à XXIV. Processus de Markov (fin). Compléments de calcul stochastique. Hermann, Paris 1992, 429 pages

Or, if you want something more "modern", there are for example

D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, 2004
P. Protter. Stochastic integration and differential equations, volume 21 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin, 2005
N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North-Holland, 1989
G. Di Nunno, B. Øksendal, and F. Proske. Malliavin Calculus for Levy Processes with Applications to Finance. Universitext. Springer-Verlag, Berlin, 2009.

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