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ISBN: 3642405258 3642405266 Year: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
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The telegraph process is a useful mathematical model for describing the stochastic motion of a particle that moves with finite speed on the real line and alternates between two possible directions of motion at random time instants. That is why it can be considered as the finite-velocity counterpart of the classical Einstein-Smoluchowski's model of the Brownian motion in which the infinite speed of motion and the infinite intensity of the alternating directions are assumed. The book will be interesting to specialists in the area of diffusion processes with finite speed of propagation and in financial modelling. It will also be useful for students and postgraduates who are taking their first steps in these intriguing and attractive fields.
Probabilities -- Mathematical models. --- Stochastic processes -- Mathematical models. --- Time-series analysis -- Mathematical models. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Options (Finance) --- Signal theory (Telecommunication) --- Electric signal theory --- Call options --- Calls (Finance) --- Listed options --- Options exchange --- Options market --- Options trading --- Put and call transactions --- Put options --- Puts (Finance) --- Statistics. --- Statistics, general. --- Electric waves --- Signal detection --- Telecommunication --- Derivative securities --- Investments --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistics .
Book
ISBN: 1461440564 1461440572 Year: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer,
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The book presents an introduction to Stochastic Processes including Markov Chains, Birth and Death processes, Brownian motion and Autoregressive models. The emphasis is on simplifying both the underlying mathematics and the conceptual understanding of random processes. In particular, non-trivial computations are delegated to a computer-algebra system, specifically Maple (although other systems can be easily substituted). Moreover, great care is taken to properly introduce the required mathematical tools (such as difference equations and generating functions) so that even students with only a basic mathematical background will find the book self-contained. Many detailed examples are given throughout the text to facilitate and reinforce learning. Jan Vrbik has been a Professor of Mathematics and Statistics at Brock University in St Catharines, Ontario, Canada, since 1982. Paul Vrbik is currently a PhD candidate in Computer Science at the University of Western Ontario in London, Ontario, Canada.
Stochastic differential equations. --- Stochastic processes -- Mathematical models. --- Stochastic processes. --- Stochastic processes --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Computer programs --- Computer programs. --- Maple (Computer file) --- Mathematics. --- Operations research. --- Management science. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistics and Computing/Statistics Programs. --- Operations Research, Management Science. --- Distribution (Probability theory. --- Mathematical statistics. --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Statistics . --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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