Votsi Irene - Multistate Models in Earthquake Modeling

We Athenians in our persons take our decisions on policy and submit them to proper discussion. The worst thing is to rush into action before the consequences have been properly debated. And this is another point where we differ from other people. We are capable at the same time of taking risks and estimating them beforehand. Others are brave out of ignorance; and when they stop to think, they begin to fear. But the man who can most truly be accounted brave is he who best knows the meaning of what is sweet in life, and what is terrible, and he then goes out undeterred to meet what is to come.

Abstract from Pericles Funeral Oration in Thucydides History of the Peloponnesian War (started in 431 B.C.)

Statistical Methods for Earthquakes Set

coordinated by

Nikolaos Limnios, Eleftheria Papadimitriou, George Tsaklidis

Volume 2

Irene Votsi

Nikolaos Limnios

Eleftheria Papadimitriou

George Tsaklidis

First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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ISTE Ltd 2019

The rights of Irene Votsi, Nikolaos Limnios, Eleftheria Papadimitriou, George Tsaklidis to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2018957211

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78630-150-5

	set of non-negative integers,
E	state space of the (semi-)Markov chain
E*	state space of the hidden Markov renewal chain
L	state space of the Markov renewal chain
A	observation space
	real matrices defined on EE
	real matrices defined on EA
	matrix-valued functions with values in and defined on
A1A2	(discrete-time) matrix convolution product on
	embedded Markov chain
	sojourn times between successive jumps
	jump times
	sequence of observations
	(semi-)Markov chain
	backward recurrence times
	double Markov chain
	Markov renewal chain
	hidden Markov renewal chain
	hidden (semi-)Markov chain
M	fixed censoring time
	observation of a trajectory in [0, M]
N(M)	jumps number of the EMC up to time M
Ni(M)	visits number of the EMC to state i up to time M
Nij(M)	jumps number of the EMC from state i to state j up to time M
N(i, s)(M)	visits number of the MRC to state (i, s) up to time M
N(i, s1)(j, s2)(M