Publication is planned for April 2004 | Hardback
| 216 pages
22 line diagrams 1 half-tone | ISBN: 0-521-82447-8
Standard texts and research in economics
and finance ignore the
absence of evidence from the analysis of
real, unmassaged market
data to support the notion of Adam Smith’s
stabilizing
Invisible Hand. The neoclassical equilibrium
model forms the
theoretical basis for the positions of the
U.S. Treasury, the
World Bank and the European Union, accepting
it as their credo.
It provides the theoretical underpinning
for globalization,
expecting to achieve the best of all possible
worlds via the
deregulation of all markets. In stark contrast,
this text
introduces a new empirically-based model
of financial market
dynamics that explains volatility, prices
options correctly and
clarifies the instability of financial markets.
The emphasis is
on understanding how real markets behave,
not how they
hypothetically ‘should’ behave. This text
is written for
physics graduate students and finance specialists,
but will also
serve as a valuable resource for those with
a less mathematical
background.
Contents
1. The moving target; 2. Neo-classical economic
theory; 3.
Probability and stochastic processes; 4.
Scaling the ivory tower
of finance; 5. Standard betting procedures
in portfolio selection
theory; 6. Dynamics of financial markets,
volatility, and option
pricing; 7. Thermodynamic analogies vs. instability
of markets; 8.
Scaling, correlations, and cascades in finance
and turbulence; 9.
Complexity.
Publication is planned for April 2004 | Hardback
| 337 pages
10 tables 95 exercises | ISBN: 0-521-83803-7
The estimation of noisily observed states
from a sequence of data
has traditionally incorporated ideas from
Hilbert spaces and
calculus based probability theory. As conditional
expectation is
the key concept, the correct setting for
filtering theory is that
of a probability space. Graduate engineers,
mathematicians and
those working in quantitative finance wishing
to use filtering
techniques will find in the first half of
this book an accessible
introduction to measure theory, stochastic
calculus, and
stochastic processes, with particular emphasis
on martingales and
Brownian motion. Exercises are included.
The book then provides
an excellent users’ guide to filtering:
basic theory is
followed by a thorough treatment of Kalman
filtering, including
recent results which extend the Kalman filter
to provide
parameter estimates. These ideas are then
applied to problems
arising in finance, genetics and population
modelling in three
separate chapters, making this a comprehensive
resource for both
practitioners and researchers.
Contents
Part I. Theory: 1. Basic Probability Concepts;
2. Stochastic
Processes; 3. Stochastic Calculus; 4. Change
of Measures; Part II.
Applications: 5. Kalman Filtering; 6. Financial
Applications; 7.
A Genetics Model; 8. Hidden Populations.
Publication is planned for April 2004 | Hardback
| 200 pages 6
line diagrams 101 exercises | ISBN: 0-521-83734-0
Publication is planned for April 2004 | Paperback|
200 pages 6
line diagrams 101 exercises | ISBN: 0-521-54619-2
Linear systems can be regarded as a causal
shift-invariant
operator on a Hilbert space of signals, and
by doing so this book
presents an introduction to the common ground
between operator
theory and linear systems theory. The book
therefore includes
material on pure mathematical topics such
as Hardy spaces, closed
operators, the gap metric, semigroups, shift-invariant
subspaces,
the commutant lifting theorem and almost-periodic
functions,
which would be entirely suitable for a course
in functional
analysis; at the same time, the book includes
applications to
partial differential equations, to the stability
and
stabilization of linear systems, to power
signal spaces (including
some recent material not previously available
in books), and to
delay systems, treated from an input/output
point of view.
Suitable for students of analysis, this book
also acts as an
introduction to a mathematical approach to
systems and control
for graduate students in departments of applied
mathematics or
engineering.
Contents
1. Operators and Hardy spaces; 2. Closed
Operators; 3. Shift-invariance
adn causality; 4, Stabilityand stabilization;
5. spaces of
persistent signals; 6. Delay systems.
Publication is planned for May 2004 | Hardback
| 240 pages 2
figures | ISBN: 0-521-83194-6
Quantum mechanics is our most successful
physical theory.
However, it raises conceptual issues that
have perplexed
physicists and philosophers of science for
decades. This book
develops a new approach, based on the proposal
that quantum
theory is not a complete, final theory, but
is in fact an
emergent phenomenon arising from a deeper
level of dynamics. The
dynamics at this deeper level is taken to
be an extension of
classical dynamics to non-commuting matrix
variables, with cyclic
permutation inside a trace used as the basic
calculational tool.
With plausible assumptions, quantum theory
is shown to emerge as
the statistical thermodynamics of this underlying
theory, with
the canonical commutation/anticommutation
relations derived from
a generalized equipartition theorem. Brownian
motion corrections
to this thermodynamics are argued to lead
to state vector
reduction and to the probabilistic interpretation
of quantum
theory, making contact with recent phenomenological
proposals for
stochastic modifications to Schrodinger dynamics.
Contents
0. Introduction and overview; 1. Trace dynamics:
the classical
Lagrangian and Hamiltonian dynamics of matrix
models; 2.
Additional generic conserved quantities;
3. Trace dynamics models
with global supersymmetry; 4. Statistical
mechanics of matrix
models; 5. The emergence of quantum field
dynamics; 6. Brownian
motion corrections to Schrodinger dynamics;
7. Discussion and
outlook.
Publication is planned for May 2004 | Hardback
| 352 pages 375
exercises | ISBN: 0-521-83687-5
Publication is planned for May 2004 | Paperback
| 352 pages 375
exercises | ISBN: 0-521-54537-4
This introduction to noncommutative noetherian
rings is
intended to be accessible to anyone with
a basic background in
abstract algebra. It can be used as a second-year
graduate text,
or as a self-contained reference. Extensive
explanatory
discussion is given, and exercises are integrated
throughout.
Various important settings, such as group
algebras, Lie algebras,
and quantum groups, are sketched at the outset
to describe
typical problems and provide motivation.
The text then develops
and illustrates the standard ingredients
of the theory: e.g.,
skew polynomial rings, rings of fractions,
bimodules, Krull
dimension, linked prime ideals. Recurring
emphasis is placed on
prime ideals, which play a central role in
applications to
representation theory. This edition incorporates
substantial
revisions, particularly in the first third
of the book, where the
presentation has been changed to increase
accessibility and
topicality. New material includes the basic
types of quantum
groups, which then serve as test cases for
the theory developed.
Contents
1. A Few Noetherian Rings; 2. Skew Polynomial
Rings; 3. Prime
Ideals; 4. Semisimple Modules, Artinian Modules,
and Torsionfree
Modules; 5. Injective Hulls; 6. Semisimple
rings of Fractions; 7.
Modules over Semiprime Goldie Rings; 8. Bimodules
and Affiliated
Prime Ideals; 9. Fully Bounded Rings; 10.
Rings and Modules of
Fractions; 11. Artinian Quotient Rings; 12.
Links Between Prime
Ideals; 13. The Artin-Rees Property; 14.
Rings Satisfying the
Second Layer Condition; 15. Krull Dimension;
16. Numbers of
Generators of Modules; 17. Transcendental
Division Algebras.