By Jacques Janssen, Raimondo Manca (auth.)

ISBN-10: 038729547X

ISBN-13: 9780387295473

ISBN-10: 0387295488

ISBN-13: 9780387295480

**Applied Semi-Markov techniques **aims to offer to the reader the instruments essential to observe semi-Markov approaches in real-life difficulties. The ebook is self-contained and, ranging from a low point of likelihood suggestions, steadily brings the reader to a deep wisdom of semi-Markov techniques. The ebook offers homogeneous and non-homogeneous semi-Markov techniques, in addition to Markov and semi-Markov rewards techniques. those thoughts are primary for lots of functions, yet they aren't as completely offered in different books at the topic as they're the following.

*Audience*

This booklet is meant for graduate scholars and researchers in arithmetic, operations examine and engineering; it could additionally entice actuaries and fiscal managers, and an individual attracted to its purposes for banks, mechanical industries for reliability features, and insurance firms.

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**Additional info for Applied Semi-Markov Processes**

**Example text**

L. 16) definedfor each coeQ, is called a trajectory or sample path of the process. It must be clearly understood that the so-called "modem" study of stochastic processes is concerned with the study of the properties of these trajectories. For example, we can affirm that if two processes X and Y are indistinguishable, then there exists a set A/^ belonging to 3 of probability 0 such that: '^co^N:XXco) = Y^(cD)yteT. 17) In other words, for each co element of the set Cl-N, the two functions t h^ X^ (co) and / h-> }^ (o)) are equal.

4 A stochastic process (or simply process) with values in the measurable space {E,i^) is a family of random variables: {X„teT} where for all t: X^:Q\-^ E, (3,X) - measurable. 10) belongs to the a -algebra 3 . 1 If(£',X) = (M,y5), the process is called a real stochastic process with values i n R ; if(£,K) = (M",y5"), it is called a real multidimensional process with values in R''. }, the process X is called a discrete time stochastic process or a random sequence; if T is the positive half real line [0,oo), the process X is called a continuous time stochastic process.

22) 8 MARTINGALES In this paragraph, we shall briefly present some topics related to the most wellknown category of stochastic processes called martingales. Let Jf be a real stochastic process defined on the filtered complete probability space ( Q , 5 , P , ( 3 , , / e r ) ) . s. s. (resp. equality. 2), the martingale equality means that the best predicted value simply is the observed value of the process at the time of predicting s. The use of martingale in finance is frequently (see Janssen and Skiadas (1995)) to model the concept of an efficient financial market.

### Applied Semi-Markov Processes by Jacques Janssen, Raimondo Manca (auth.)

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