Point Process Theory and Applications: Marked Point and Piecewise Deterministic ProcessesSpringer Science & Business Media, 15 dic 2005 - 328 páginas The book aims at presenting a detailed and mathematically rigorous exposition of the theory and applications of a class of point processes and piecewise deterministic p- cesses. The framework is suf?ciently general to unify the treatment of several classes of stochastic phenomena: point processes, Markov chains and other Markov processes in continuous time, semi-Markov processes, queueing and storage models, and li- lihood processes. There are applications to ?nance, insurance and risk, population models, survival analysis, and congestion models. A major aim has been to show the versatility of piecewise deterministic Markov processes for applications and to show how they may also become useful in areas where thus far they have not been much in evidence. Originally the plan was to develop a graduate text on marked point processes - dexed by time which would focus on probabilistic structure and be essentially se- contained. However, it soon became apparent that the discussion should naturally include a traditional class of continuous time stochastic processes constructed from certain marked point processes. This class consists of ‘piecewise deterministic p- cesses’; that is, processes with ?nitely many jumps on ?nite time intervals which, roughly speaking, develop deterministically between the random jump times. The - position starts with the point process theory and then uses this to treat the piecewise deterministic processes. |
Índice
II | 3 |
III | 5 |
IV | 9 |
VI | 11 |
VII | 17 |
IX | 21 |
X | 25 |
XI | 33 |
XXXIII | 167 |
XXXIV | 170 |
XXXV | 177 |
XXXVI | 184 |
XXXVII | 203 |
XXXVIII | 217 |
XXXIX | 225 |
XL | 231 |
XIII | 41 |
XIV | 50 |
XV | 63 |
XVI | 68 |
XVII | 77 |
XVIII | 85 |
XIX | 94 |
XX | 103 |
XXII | 110 |
XXIII | 119 |
XXV | 123 |
XXVI | 143 |
XXVIII | 146 |
XXIX | 152 |
XXX | 163 |
XXXI | 165 |
XLII | 235 |
XLIII | 243 |
XLIV | 247 |
XLV | 251 |
XLVI | 257 |
XLVII | 267 |
XLVIII | 277 |
XLIX | 287 |
L | 297 |
LI | 301 |
309 | |
315 | |
LIV | 321 |
LV | 325 |
Otras ediciones - Ver todo
Point Process Theory and Applications: Marked Point and Piecewise ... Martin Jacobsen Vista previa restringida - 2006 |
Términos y frases comunes
arbitrary assume bounded cadlag canonical compensating measure conditional distribution consider continuous counting measures counting process defined definition denote determined differentiable equation Example F-compensating filtration finite follows given H₁ hazard function hazard measure holds homogeneous PDMP homogeneous Poisson independent increments integral intensity process interval invariant probability Itô's formula Lemma Let Q Lévy process likelihood process local martingale M₁ mark space Markov chain Markov kernels Markov process Markov property martingale measure N₁ Note o-algebra particular path-open piecewise deterministic Pixo Poisson process Poisson random measure probability space proof Proposition Q-martingale queue R-valued random variables right-continuous satisfy self-financing sequence stochastic Suppose T₁ Theorem Tn+1 transition probabilities V₁ vector X₁ Zn xo ξη