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% References on stochastic differential equations
% 2004:12:09 CWI
% Jan H. van Schuppen

The following reference is of introductory nature,
it is useful for readers who have never studied 
stochastic differential equations before.
After reading this book the more mathematically inclined 
readers may want to read mathematically more developed books.

% JGB: in CWI library under Oek
@book{oksendal:2003,
author =      {B. \Oksendal},
title =       {Stochastic differential equations (6th Ed.)},
series =      {Universitext},
number =      {},
publisher =   {Springer},
address =     {Berlin},
year =        {2003},
pages =       {360},
isbn =        {3-540-04758-1},
price =       {EUR 34,95},
affiliation = {University of Oslo, Norway},
note =        {},
cwilib =      {},
class =       {m60h10, m600xx}
}

The following books are a major source on martingale
theory and stochastic integration. The French editions
of the first two volumes are also listed.

@book{dellacherie:meyer:1978,
author = "C. Dellacherie and P.-A. Meyer",
title = "Probabilities and potentials, 3 volumes",
publisher = "North-Holland",
address = "Amsterdam",
year = "1978-1988",
class = "m60002" 
}

@book{dellacherie:meyer:1975,
author = "C. Dellacherie and P.A. Meyer",
title = {Probabilit\'{e}s et potentiel, CH. I \`{a} IV},
publisher = "Hermann",
address = "Paris",
year = "1975",
class = "jhvsb m01z00 m60002 m60g07"
}

@book{dellacherie:meyer:1980,
author = "C. Dellacherie and P.A. Meyer",
title = "{Probabilit\'{e}s et potentiel, Ch. V \'{a} VIII}",
publisher = "Hermann",
address = "Paris",
year = "1980",
class = "jhvsb m01z00 m60002 m60gxx"
}
    
The next book is a well known source on stochastic
differential equations driven by Brownian motion processes.
The general theory of stochastic processes and martingale
theory is less developed than in the books by
Dellacherie and Meyer.
 
@book{karatzas:shreve:1987,
author = "I. Karatzas and S. Shreve",
title = "Brownian motion and stochastic calculus",
publisher = "Springer-Verlag",
address = "Berlin",
year = "1987",
class = "jhvsb m60002"
}

The following book is older but has much on the
partial differential equations of the densities
of solutions of stochastic differential equations.

@book{dynkin:1965,
author = "E.B. Dynkin",
title = "{Markov} processes, volume 1, volume 2",
publisher = "Academic Press Inc., Publishers",
address = "New York",
year = "1965",
class = "jhvsb m01z00 m60002 m60jxx"
}

The following book is rather specialized, to limit theorems.
However, the first part of the book contains an extensive
introduction and summary of the general theory of
stochastic processes, martingale theory, stochastic
integrals, and the stochastic calculus rule.
It does not have much on stochastic differential equations.
Both sample continuous and jump processes are treated
in a general format and the presentation is more modern 
than the books listed above. The level in general is 
really excellent.

@book{jacod:shiryaev:2003,
author =      {Jean Jacod and Albert N. Shiryaev},
title =       {Limit theorems for stochastic processes (2nd. Ed.)},
series =      {},
number =      {},
publisher =   {Springer},
address =     {Berlin},
year =        {2003},
pages =       {},
isbn =        {3 540 43932 3},
price =       {},
affiliation = {Universite de Paris VI, Paris, France;
               Steklov Mathematical Institute, Russian Academy of
               Sciences, Moscow, Russia},
note =        {},
cwilib =      {},
class =       {jhvsb},
keywords =    {stochastic processes, martingale theory,
               predictable characteristics, limit theorems}
}

The following book is rather specialized.    

@book{ikeda:watanabe:1981,
author = "N. Ikeda and S. Watanabe",
title = "Stochastic differential equations and diffusion processes",
publisher = "North-Holland Publ. Co.",
address = "Amsterdam",
year = "1981",
class = "jhvsb m01z00 m60002 m60hxx m60jxx"
}

The next reference is a paper on a particular stochastic
partial differential equation. 

@article{pardoux:1979,
author = "E. Pardoux",
title = "Stochastic partial differential equations
   and filtering of diffusion processes",
journal = "Stochastics",
volume = "3",
year = "1979",
pages = "127-167",
class = "m93p28"
}

The next reference is the major source in book form for numerical
approximation of the solutions of stochastic differential
equations.

@book{kloeden:platen:1992,
author = "P.E. Kloeden and E. Platen",
title = "Numerical solution of stochastic differential equations",
publisher = "Springer",
address = "Berlin",
year = "1992",
class = "m65c30 m60h10" 
}

The following reference is the main source for the
numerical approximation of solutions of stochastic
control and filtering problems.

@book{kushner:dupuis:2001,
author =      {H.J. Kushner and P.G. Dupuis},
title =       {Numerical methods for stochastic control problems
               in continuous time (2nd Ed.)},
series =      {Applications of Mathematics},
number =      {24},
publisher =   {Springer},
address =     {New York},
year =        {2001},
pages =       {488},
isbn =        {0-387-95139-3},
price =       {USD 69.95},
affiliation = {Brown University, Providence, RI},
note =        {},
class =       {m93jrqsj}
}

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