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An Introduction to Stochastic Processes with Applications to Biology
Linda J. S. Allen
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eBook - PDF
An Introduction to Stochastic Processes with Applications to Biology
Linda J. S. Allen
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Table of contents
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About This Book
An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and
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Chapter
1
Review
of
Probability
Theory
and
an
Introduction
to
Stochastic
Processes
1.1
Introduction
The
underlying
mathematical
theory
of
stochastic
modeling
lies
within
stochastic
processes
.
The
theory
of
stochastic
processes
is
based
on
proba-
bility
theory.
Therefore,
this
ļ¬rst
chapter
is
a
brief
review
of
some
basic
prin-
ciples
from
probability
theory.
An
excellent
reference
for
stochastic
processes
with
applications
to
biology
is
the
classic
textbook
by
Bailey,
The
Elements
of
Stochastic
Processes
with
Applications
to
the
Natural
Sciences
,
which
has
been
referenced
frequently
since
its
initial
publication
in
1964
and
is
cited
frequently
in
this
book
as
well.
John
Wiley
&
Sons
republished
this
clas-
sic
textbook
in
1990
and
it
is
this
reference
that
is
cited.
Other
references
for
various
types
of
stochastic
processes
are
listed
at
the
end
of
each
of
the
chapters.
It
is
the
goal
of
this
book
to
introduce
the
basic
theory
of
stochastic
pro-
cesses
necessary
in
understanding
and
applying
these
methods
to
biological
problems,
such
as
population
extinction,
enzyme
kinetics,
two-species
com-
petition
and
predation,
spread
of
epidemics,
and
the
genetics
of
inbreeding.
Some
of
the
classical
stochastic
models
from
biology
have
a
deterministic
counterpart.
For
these
models,
the
dynamics
of
the
deterministic
model
will
be
discussed
and
compared
to
that
of
the
corresponding
stochastic
model.
One
of
the
most
important
diļ¬erences
between
deterministic
and
stochas-
tic
models
is
that
deterministic
models
predict
an
outcome
with
absolute
certainty,
whereas
stochastic
models
provide
only
the
probability
of
an
out-
come.
Stochastic
models
take
into
account
the
variability
in
the
process
due
to
births,
deaths,
transitions,
emigration,
immigration,
and
environmental
variability
that
impact
the
biological
process.
For
example,
a
deterministic
model
for
a
population
of
cells,
animals,
plants,
or
genes
is
often
expressed
in
terms
of
diļ¬erence
equations
or
diļ¬erential
equations
which
follow
the
growth
and
decline
in
the
size
of
the
populations
over
time.
The
solution
of
these
equations
follows
a
prescribed
path
or
trajectory
over
time.
Given
a
ļ¬xed
ini-
tial
population
size,
a
unique
deterministic
solution
will
follow
the
same
path
over
time.
A
stochastic
model
of
a
population
process
may
also
be
expressed
1
Table of contents
- Cover
- Dedication
- Preface to the First Edition
- Preface to the Second Edition
- Contents
- List of Tables
- List of Figures
- Chapter 1: Review of Probability Theory and an Introduction to Stochastic Processes
- Chapter 2: Discrete-Time Markov Chains
- Chapter 3: Biological Applications of Discrete-Time Markov Chains
- Chapter 4: Discrete-Time Branching Processes
- Chapter 5: Continuous-Time Markov Chains
- Chapter 6: Continuous-Time Birth and Death Chains
- Chapter 7: Biological Applications of Continuous-Time Markov Chains
- Chapter 8: Diffusion Processes and Stochastic Differential Equations
- Chapter 9: Biological Applications of Stochastic Differential Equations
- Appendix A: Hints and Solutions to Selected Exercises
- Back Cover
Citation styles for An Introduction to Stochastic Processes with Applications to Biology
APA 6 Citation
Allen, L. (2010). An Introduction to Stochastic Processes with Applications to Biology (2nd ed.). CRC Press. Retrieved from https://www.perlego.com/book/1509211/an-introduction-to-stochastic-processes-with-applications-to-biology-pdf (Original work published 2010)
Chicago Citation
Allen, Linda. (2010) 2010. An Introduction to Stochastic Processes with Applications to Biology. 2nd ed. CRC Press. https://www.perlego.com/book/1509211/an-introduction-to-stochastic-processes-with-applications-to-biology-pdf.
Harvard Citation
Allen, L. (2010) An Introduction to Stochastic Processes with Applications to Biology. 2nd edn. CRC Press. Available at: https://www.perlego.com/book/1509211/an-introduction-to-stochastic-processes-with-applications-to-biology-pdf (Accessed: 25 September 2021).
MLA 7 Citation
Allen, Linda. An Introduction to Stochastic Processes with Applications to Biology. 2nd ed. CRC Press, 2010. Web. 25 Sept. 2021.