I need some good books that have good examples in each chapters of book. Could you please offer me some good books?
For probability theory and stochastic processes you need to read the books by Shiryaev and Skorohod:
- A. N. Shiryaev, Probability, volume 95 of graduate texts in Mathematics
- A. V. Skorohod, Limits Theorem for Stochastic
Processes, Teorija Verojatnosteii Primenenija, 1 (1956) 289-319.
- A. V. Skorohod, Studies in the Theory of Random
Processes. Translated form the Russian, scripta Technica, Inc.,
Addison-Wesley Publishing Co., Inc., Reading, MA, (1965).
and for everything else you need to consult the following books and articles from your library:
- H. Brezis, Functional Analysis, Sobolev spaces and Partial Differential Equations, Springer, 2010.
- C. Dellacherie, P. A. Meyer, Probability and Potential, North-Holland, Amsterdam, 1979.
- N. Ikeda and S. Watanabe, Stochastic differential
equations and diffusion processes, North-Holland Publishing Co.,
Amsterdam-New York, 1981.
- N. V. Krylov and B. L. Rozovskii, Stochastic Evolution
Equations, Stochastic Differential Equations: theory and applications, 1-69,
Interdiscip. Math. Sci., 2, World Sci. Pub., Hackensack, NJ, 2007.
- Ondrejat, Martin Uniqueness for stochastic evolution
equations in Banach spaces. Dissertationes Math. (Rozprawy Mat.) 426, 63 pp,
2004.
- Yu.V. Prohorov. Convergence of random processes and
limits theorems in probability theory. (Russian), Teor. Veroyatnost. i
Primen, 1, 177-238, 1956.
W. Arendt, Vector-valued Laplace Transforms and Cauchy problems, 2nd Ed. Birkhauser.
Thank you very much, it is a good book, but doesn't have any example!
Hello Roya,
The book by Donald L. Cohn, Measure Theory, is a nice reference. You can get a copy from libgen.io
http://libgen.io/book/index.php?md5=2F37E55C5A9B4F14C5E64697DCF71306
Hello Roya,
This book may be helpful for functional analysis,
Infinite Dimensional Analysis: A Hitchhiker's Guide
by Aliprantis and Border.
Best,
Karl
Hello Roya,
see, J. Diestel and J.J. Uhl, Jr., Vector Measures, American Mathematical Society
for Bochner integral and related topics.
http://www.ams.org/books/surv/015/surv015-endmatter.pdf
(sample)
I would suggest you check out:
- Variational Analysis by T. Rockafellar and Wets (for setvalued analysis)
- Probability and Measure by P. Billingsley
-Functional Analysis by W. Rudin
- For Bochner Intregrals you can check the enclosed link
Article Stochastic integration in Banach spaces and applications to ...
You can check out volume 1 of our new book. The preprint version can be downloaded from:
http://fa.its.tudelft.nl/~neerven/ABS/volume1_Hytonen_Neerven_Veraar_Weis.pdf
For probability theory and stochastic processes you need to read the books by Shiryaev and Skorohod:
- A. N. Shiryaev, Probability, volume 95 of graduate texts in Mathematics
- A. V. Skorohod, Limits Theorem for Stochastic
Processes, Teorija Verojatnosteii Primenenija, 1 (1956) 289-319.
- A. V. Skorohod, Studies in the Theory of Random
Processes. Translated form the Russian, scripta Technica, Inc.,
Addison-Wesley Publishing Co., Inc., Reading, MA, (1965).
and for everything else you need to consult the following books and articles from your library:
- H. Brezis, Functional Analysis, Sobolev spaces and Partial Differential Equations, Springer, 2010.
- C. Dellacherie, P. A. Meyer, Probability and Potential, North-Holland, Amsterdam, 1979.
- N. Ikeda and S. Watanabe, Stochastic differential
equations and diffusion processes, North-Holland Publishing Co.,
Amsterdam-New York, 1981.
- N. V. Krylov and B. L. Rozovskii, Stochastic Evolution
Equations, Stochastic Differential Equations: theory and applications, 1-69,
Interdiscip. Math. Sci., 2, World Sci. Pub., Hackensack, NJ, 2007.
- Ondrejat, Martin Uniqueness for stochastic evolution
equations in Banach spaces. Dissertationes Math. (Rozprawy Mat.) 426, 63 pp,
2004.
- Yu.V. Prohorov. Convergence of random processes and
limits theorems in probability theory. (Russian), Teor. Veroyatnost. i
Primen, 1, 177-238, 1956.
W. Arendt, Vector-valued Laplace Transforms and Cauchy problems, 2nd Ed. Birkhauser.
For probability and stochastic processes I recommend the Karlin-Taylor series of books out of Stanford.
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