A01=M.H.A. Davis
advanced stochastic modeling applications
Arbitrary Index Set
Author_M.H.A. Davis
Banach Space
Borel Cantelli Lemma
Borel Sets
Category=PBT
Category=PBWL
Conditional Expectation
continuous time systems
dimensional
distributions
Dynkin Formula
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Feller Process
Filtered Probability Space
finite
Finite Dimensional Distributions
impulse control methods
Jump Process
Lipschitz Continuous
local
Local Martingale
M.H.A. Davis
Markov Processes
martingale
optimal resource allocation
Optional Sampling Theorem
piecewise deterministic processes
probability
process
property
queueing system analysis
Sample Path
space
stochastic control theory
strong
Strong Markov Property
Virtual Waiting Time
Product details
- ISBN 9780412314100
- Weight: 740g
- Dimensions: 152 x 229mm
- Publication Date: 01 Aug 1993
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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This book presents a radically new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems. This approach is based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stochastic system models. A PDP is a Markov process that follows deterministic trajectories between random jumps, the latter occurring either spontaneously, in a Poisson-like fashion, or when the process hits the boundary of its state space. This formulation includes an enormous variety of applied problems in engineering, operations research, management science and economics as special cases; examples include queueing systems, stochastic scheduling, inventory control, resource allocation problems, optimal planning of production or exploitation of renewable or non-renewable resources, insurance analysis, fault detection in process systems, and tracking of maneuvering targets, among many others.
The first part of the book shows how these applications lead to the PDP as a system model, and the main properties of PDPs are derived. There is particular emphasis on the so-called extended generator of the process, which gives a general method for calculating expectations and distributions of system performance functions. The second half of the book is devoted to control theory for PDPs, with a view to controlling PDP models for optimal performance: characterizations are obtained of optimal strategies both for continuously-acting controllers and for control by intervention (impulse control). Throughout the book, modern methods of stochastic analysis are used, but all the necessary theory is developed from scratch and presented in a self-contained way. The book will be useful to engineers and scientists in the application areas as well as to mathematicians interested in applications of stochastic analysis.
