This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.

This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.

From a review of the first edition: "This book […] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. Papangelou, Zentralblatt MATH) The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.

This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics. It comprises the material of a one-year course, which is addressed to students of mathematics and to scientists with an interest in the mathematical side of stochastics.The stochastic concepts, models and methods are motivated by examples and then developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems, now in part with solutions, offer applications and supplements to the text.

This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics. It comprises the material of a one-year course, which is addressed to students of mathematics and to scientists with an interest in the mathematical side of stochastics.The stochastic concepts, models and methods are motivated by examples and then developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems, now in part with solutions, offer applications and supplements to the text.

Dieses Lehrbuch gibt eine Einführung in die "Mathematik des Zufalls", bestehend aus den beiden Teilbereichen Wahrscheinlichkeitstheorie und Statistik. Die stochastischen Konzepte, Modelle und Methoden werden durch typische Anwendungsbeispiele motiviert und anschließend systematisch entwickelt. Der dafür notwendige maßtheoretische Rahmen wird gleich zu Beginn auf elementarem Niveau bereitgestellt. Zahlreiche Übungsaufgaben, zum Teil mit Lösungsskizzen, illustrieren und ergänzen den Text. Zielgruppe sind Studierende der Mathematik ab dem dritten Semester, sowie Naturwissenschaftler und Informatiker mit Interesse an den mathematischen Grundlagen der Stochastik.

Die 5. Auflage wurde nochmals bearbeitet und maßvoll ergänzt.

This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.

This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.

From a review of the first edition: "This book […] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. Papangelou, Zentralblatt MATH) The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.

This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics. It comprises the material of a one-year course, which is addressed to students of mathematics and to scientists with an interest in the mathematical side of stochastics.The stochastic concepts, models and methods are motivated by examples and then developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems, now in part with solutions, offer applications and supplements to the text.

This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics. It comprises the material of a one-year course, which is addressed to students of mathematics and to scientists with an interest in the mathematical side of stochastics.The stochastic concepts, models and methods are motivated by examples and then developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems, now in part with solutions, offer applications and supplements to the text.

Dieses Lehrbuch gibt eine Einführung in die "Mathematik des Zufalls", bestehend aus den beiden Teilbereichen Wahrscheinlichkeitstheorie und Statistik. Die stochastischen Konzepte, Modelle und Methoden werden durch typische Anwendungsbeispiele motiviert und anschließend systematisch entwickelt. Der dafür notwendige maßtheoretische Rahmen wird gleich zu Beginn auf elementarem Niveau bereitgestellt. Zahlreiche Übungsaufgaben, zum Teil mit Lösungsskizzen, illustrieren und ergänzen den Text. Zielgruppe sind Studierende der Mathematik ab dem dritten Semester, sowie Naturwissenschaftler und Informatiker mit Interesse an den mathematischen Grundlagen der Stochastik.

Die 5. Auflage wurde nochmals bearbeitet und maßvoll ergänzt.