This
textbook gives a comprehensive introduction to stochastic processes and
calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus
and processes have gained great importance, because they play a
decisive role in the modeling of financial markets and as a basis for
modern time series econometrics. Mathematical theory is applied to solve
stochastic differential equations and to derive limiting results for
statistical inference on nonstationary processes.
This
introduction is elementary and rigorous at the same time. On the one
hand it gives a basic and illustrative presentation of the relevant
topics without using many technical derivations. On the other hand many
of the procedures are presented at a technically advanced level: for a
thorough understanding, they are to be proven. In order to meet both
requirements jointly, the present book is equipped with a lot of
challenging problems at the end of each chapter as well as with the
corresponding detailed solutions. Thus the virtual text - augmented with
more than 60 basic examples and 40 illustrative figures - is rather
easy to read while a part of the technical arguments is transferred to
the exercise problems and their solutions.
1 Introduction . . . . . . . . . . . . . . . . . . . . . 1
1.1 Summary.. . . . . . . . . . . . . . . . . . . . . . 1
1.2 Finance. . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Econometrics . . . . . . . . . . . . . . . . . . . . . 3
1.4 Mathematics . . . . . . . . . . . . . . . . . . . . . 6
1.5 Problems and Solutions . . . . . . . . . . . 7
Part I Time Series Modeling
2 Basic Concepts from Probability Theory . . . . 13
2.1 Summary.. . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Random Variables . . . . . . . . . . . . . . . . . . . . 13
2.3 Joint and Conditional Distributions . . . . . 22
2.4 Stochastic Processes (SP) . . . . . . . . . . 29
2.5 Problems and Solutions . . . . . . . . . . . . . . . . 35
3 AutoregressiveMoving Average Processes (ARMA). . . 45
3.1 Summary. . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Moving Average Processes . . . . . . . . . . 45
3.3 Lag Polynomials and Invertibility . . . . . 51
3.4 Autoregressive and Mixed Processes . 56
3.5 Problems and Solutions . . . . . . . . . . . 68
4 Spectra of Stationary Processes . . . . . . . . . . . . 77
4.1 Summary.. . . . . . . . . . . . . . . . . . . . . 77
4.2 Definition and Interpretation . . . . . . . . 77
4.3 Filtered Processes . . . . . . . . . . . . . . . . . . . . 84
4.4 Examples of ARMA Spectra . . . . . 89
4.5 Problems and Solutions . . . . . . . . . . 95
5 Long Memory and Fractional Integration 103
5.1 Summary. . . . . . . . . . . . . . . . . . . 103
5.2 Persistence and Long Memory . . . . 103
5.3 Fractionally Integrated Noise . . . . . . . 108
5.4 Generalizations . . . . . . . . . . . . . . . . . . 113
5.5 Problems and Solutions . . . . . . . . . 118
6 Processes with Autoregressive Conditional Heteroskedasticity (ARCH) 127
6.1 Summary.. . . . . . . . . . . . . . . . . . . . 127
6.2 Time-Dependent Heteroskedasticity 127
6.3 ARCH Models . . . . . . . . . . . . . . . 130
6.4 Generalizations . . . . . . . . . . . . . . . . . . 135
6.5 Problems and Solutions . . . . . . . . . . 142
Part II Stochastic Integrals
7 Wiener Processes (WP) . . . . . . . . . . . . . . . 151
7.1 Summary . . . . . . . . . . . . . . . . . . . . . 151
7.2 From RandomWalk to Wiener Process . . . . 151
7.3 Properties . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.4 Functions of Wiener Processes . . . . . . 161
7.5 Problems and Solutions . . . . . . . . . . . . . 170
8 Riemann Integrals . . . . . . . . . . . . . . . . . . . . . . 179
8.1 Summary . . . . . . . . . . . . . . . . . . . . 179
8.2 Definition and Fubini’s Theorem . . . 179
8.3 Riemann Integration ofWiener Processes . . . . 183
8.4 Convergence in Mean Square . . . . . . . 186
8.5 Problems and Solutions . . . . . . . . . . . 190
9 Stieltjes Integrals . . . . . . . . . . . . . . . . . . . . . 199
9.1 Summary . . . . . . . . . . . . . . . . . . . . 199
9.2 Definition and Partial Integration . . . . . 199
9.3 Gaussian Distribution and Autocovariances . . . 202
9.4 Standard Ornstein-Uhlenbeck Process . . 204
9.5 Problems and Solutions . . . . . . . . . . . 207
10 Ito Integrals . . . . . . . . . . . . . . . . . . . . . . 213
10.1 Summary . . . . . . . . . . . . . . . . 213
10.2 A Special Case . . . . . . . . . . . . . . . . . . 213
10.3 General Ito Integrals . . . . . . . . . . . . 218
10.4 (Quadratic) Variation . . . . . . . . . . . . 222
10.5 Problems and Solutions . . . . . . . . . . 229
11 Ito’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . 239
11.1 Summary . . . . . . . . . . . . . . . . . . . 239
11.2 The Univariate Case . . . . . . . . . . . . . . . 239
11.3 Bivariate Diffusions with One WP . . . . 245
11.4 Generalization for IndependentWP . . 250
11.5 Problems and Solutions . . . . . . . . . . . 254
Part III Applications
12 Stochastic Differential Equations (SDE) . . . . 261
12.1 Summary . . . . . . . . . . . . . . . . . . . 261
12.2 Definition and Existence . . . . . . . . . . . 261
12.3 Linear Stochastic Differential Equations 265
12.4 Numerical Solutions . . . . . . . . . . . . . . . . 272
12.5 Problems and Solutions . . . . . . . . . . 273
13 Interest Rate Models . . . . . . . . . . . . . . . . . . 285
13.1 Summary . . . . . . . . . . . . . . . . . . . . 285
13.2 Ornstein-Uhlenbeck Process (OUP) . . 285
13.3 Positive Linear Interest Rate Models . . . 288
13.4 Nonlinear Models . . . . . . . . . . . . . . . 292
13.5 Problems and Solutions . . . . . . . . . . . 296
14 Asymptotics of Integrated Processes . . . . . . . . . 303
14.1 Summary . . . . . . . . . . . . . . . . . . . . . 303
14.2 Limiting Distributions of Integrated Processes 303
14.3 Weak Convergence of Functions . . . . 310
14.4 Multivariate Limit Theory . . . . . . . . . . . . . 317
14.5 Problems and Solutions . . . . . . . . . . . . . . . 321
15 Trends, Integration Tests and Nonsense Regressions 331
15.1 Summary . . . . . . . . . . . . . . . . . . 331
15.2 Trend Regressions . . . . . . . . . . . . . 331
15.3 Integration Tests . . . . . . . . . . . . . . . . 336
15.4 Nonsense Regression . . . . . . . . . . . . . . . 341
15.5 Problems and Solutions . . . . . . . . . . 344
16 Cointegration Analysis . . . . . . . . . . . . . . . . . 353
16.1 Summary . . . . . . . . . . . . . . . . 353
16.2 Error-Correction and Cointegration . . 353
16.3 Cointegration Regressions . . . . . . . . 358
16.4 Cointegration Testing . . . . . . . . . . . 365
16.5 Problems and Solutions . . . . . . . . . 373
This
book captures the complex world of planetary moons, which are more
diverse than Earth's sole satellite might lead you to believe. New
missions continue to find more of these planetary satellites, making an
up to date guide more necessary than ever. Why do Mercury and Venus have
no moons at all? Earth's Moon, of course, is covered in the book with
highly detailed maps. Then we move outward to the moons of Mars, then on
to many of the more notable asteroid moons, and finally to a list of
less-notable ones.
All the major moons of the gas giant planets
are covered in great detail, while the lesser-known satellites of these
worlds are also touched on. Readers will learn of the remarkable
trans-Neptunian Objects – Pluto, Eris, Sedna, Quaoar –including many of
those that have been given scant attention in the literature. More than
just objects to read about, the planets' satellites provide us with
important information about the history of the solar system.
Projects to help us learn more about the moons are included throughout
the book. Most amateur astronomers can name some of the more prominent
moons in the solar system, but few are intimately familiar with the full
variety that exists in our backyard: 146 and counting. As our
understanding of the many bodies in our solar system broadens, this is an invaluable tour of our expanding knowledge of the moons both near and far.
Part I. Moons
1. Mercury and Venus .......................... 3
Why No Real Moons? ........................ 3
Mercury .................................... 3
Venus .................................. 4
2. Earth and Luna .......................... 7
Luna .................................................. 7
Formation and Origin ................. 7
Impact on Earth .................................. 10
Selected Lunar Features .................... 13
Descriptions .................................... 22
Other Near Earth Objects ................. 51
3. Mars ...................................... 59
Phobos ........................................... 62
Deimos ........................................... 63
Trojans ............................................. 65
Mars Crossers/Hungaria Family ..................... 66
4. The Asteroid Belt .................................. 69
The Main Belt ......................................... 69
Comets .............................................. 70
Main-Belt Asteroids/Hungaria Family ................. 71
A Final Note ................................ 80
5. Jupiter ................................. 81
Rings .................................................... 81
Amalthea (or Inner) Group ................. 84
The Galilean Moons .............................. 87
Io .................................................... 88
Europa .......................................... 92
Ganymede ................................... 94
Callisto ................................... 95
Themisto ..................................... 98
Himalia Group ................................. 98
Carpo ............................................ 100
S/2003 J 12 and S/2011 J 1 .............. 100
Ananke Group ...................................... 100
Carme Group .......................... 100
Pasiphae Group ............................ 101
S/2003 J 2 ....................................... 102
Jupiter Trojans ................................... 102
6. Saturn ......................................... 105 Types of Moons ........................... 108
Alkyonides ............................ 108
Co-orbital ................................... 108
Dynamical Families................... 108
Inner Moons ............................ 108
Outer Moons ......................... 109
Shepherd Moons ....................... 109
Trojan Moons ...................... 110
Descriptions .................................. 110
Very Minor Moons Not Classed Elsewhere ........... 110
Minor Moons Not Classed Elsewhere ................ 113
Mimas....................................... 120
Enceladus ..................... 122
Tethys .............................. 125
Dione ........................... 126
Rhea .................................. 130
Titan .............................. 134
Hyperion ......................... 139
Iapetus ............................. 141
Phoebe ............................... 143
Gallic Group ....................... 145
Inuit Group ......................... 146
Norse Group ............................ 146
Chiron ..................... 147
Themis ............................ 147
Others ............................... 148
7. Uranus ................................ 149
Descriptions ........................... 149
Moon Discoveries? ................. 152
Inner Moons ........................ 152
Miranda ................ 158
Ariel ..................................... 159
Umbriel .............................. 161
Titania ......................... 162
Oberon ........................... 164
Irregular Moons .................. 166
Margaret ............................. 168
8. Neptune ..................................... 171
Descriptions .......................... 171
Inner Moons .......................... 171
Triton ................................ 177
Nereid ........................................ 181
Retrograde Irregular Moons ........... 182
Prograde Irregular Moons ........... 183
9. Distant Minor Planets ............. 185
Cis-Neptunian Objects ................. 185
TNOs ................................... 185
Centaurs with Moons ............ 187
Cubewanos with Moons ................ 192
Plutinos with Moons ............... 193
RTNOs with Moons ................ 196
SDOs with Moons ........................ 196
Part II. Projects
10. Logging/Blogging ....................... 199
What to Record ................... 199
Computers .............................. 201
11. c: The Speed of Light ............. 203
Measuring Space with Numbers ......... 203
The Speed of Light: A Brief History ........... 204
So What Is the Speed of Light in a Vacuum? ...... 205
Playing with the Speed of Light ..................... 205
12. Telescopic Moon Targets ........... 211
Observation ............................... 211
Jupiter and Its Moons ................... 212
Age and Vision ....................... 212
Darkness .......................... 213
Distance .................. 213
Glare ..................................... 214
Trying It Out .......................... 214
13. Life on Moon Worlds ................... 217
An Alternative Lifestyle? ........... 217
Habitability Concerns ............... 217
Temporal Concerns .................... 220
Vacation Among the Stars .......... 221
Io ............................ 221
Saturn .......................... 221
Uranus ........................ 223
Triton .............................. 223
14. Citizen Science ................ 225
Distributed Computing ............... 225
Citizen Science .................... 226
Remote Observing ................... 227
Google Moon ........................ 227
The
United Nations adoption of the Convention on the Rights of Persons with
Disabilities (CRPD) constituted a paradigm shift in attitudes and
approaches to disability rights,
marking the first time in law-making history that persons with
disabilities participated as civil society representatives and
contributed to the drafting of an international treaty. On the way, they
brought a new kind of diplomacy forward: empowering nongovernmental
stakeholders, including persons with disabilities, within human rights
discourse. This landmark treaty provides an opportunity to consider
what it means to involve members of a global civil society in UN-level
negotiations.
Human Rights and Disability Advocacy brings
together perspectives from individual representatives of the Disabled
People's Organizations (DPOs), nongovernmental organizations (NGOs),
indigenous peoples' organizations, states, and national institutions
that played leading roles in the Convention's drafting process. The
contributors provide vivid and personal accounts of the paths to
victory, including stumbling blocks not all of which were overcome and
offer a unique look into the politics of civil society organizations
both from within and in its interaction with governments. Each essay
describes the nonnegotiable key issues for which they advocated; the
extent of success in reaching their goals; and insights into the
limitations they faced. Through the plurality of voices and insider
perspectives, Human Rights and Disability Advocacy presents fresh
perspectives on the shift toward a new diplomacy and explores the
implication of this model for human rights advocacy more generally.
Contributors:
Andrew Byrnes, Heidi Forrest, Phillip French, Lex Grandia, Huhana
Hickey, Markku Jokinen, Liisa Kauppinen, Mi Yeon Kim, Gerison Lansdown,
Connie Laurin-Bowie, Tirza Leibowitz, Don MacKay, Anna MacQuarrie,
Ronald C. McCallum AO, Tara J. Melish, Pamela Molina Toledo, Maya
Sabatello, Marianne Schulze, Belinda Shaw.
1. A Short History of the International Disability Rights
Movement 13
Maya Sabatello
2. Our Lives, Our Voices: People with Intellectual Disabilities
and Their Families 25
Anna MacQuarrie and Connie Laurin-Bowie
3. Living in the Community, Access to Justice: Having the
Right Makes All the Difference 45
Tirza Leibowitz
4. Inclusion or Choice? Securing the Right to Inclusive
Education for All 58
Belinda Shaw
5. An Eye Toward Effective Enforcement: A Technical- Comparative
Approach to the Drafting Negotiations 70
Tara J. Melish
6. Children with Disabilities 97
Gerison Lansdown
7. Women with Disabilities: Th e Convention Through the
Prism of Gender 113
Mi Yeon Kim
8. Including Deaf Culture and Linguistic Rights 131
Liisa Kauppinen and Markku Jokinen
9. Imagine: To Be a Part of Th is 146
Lex Grandia
10. Indigenous People with Disabilities: The Missing Link 157
Huhana Hickey
11. At the United Nations . . . “Th e South Also Exists” 170
Pamela Molina Toledo
12. Voices Down Under: An Australian Perspective 188
Heidi Forrest and Phillip French
13. Monitoring the Convention’s Implementation 209
Marianne Schulze
14. Th e Role of National Human Rights Institutions 222
Andrew Byrnes
15. Th e New Diplomacy 239
Maya Sabatello
