This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the presence of time-dependent absorption and excitation. The book is suitable as an advanced textbook for graduate courses.
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"This book is a very welcome contribution to the growing literature on this fascinating field ... It is clearly written and therefore accessible to graduate students and researchers with a solid background in analysis ... It will certainly attract many new researchers to a field which had, curiously, a very slow start but seems now ready to reach its maturity, both on the theoretical and applied sides."Mathematical Reviews
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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weak fundamental solution, backward propagator, next assertion concerns, stochastic continuity condition, uniform parabolicity condition, final value problem, capacitability theorem, transition probability function, separability set, differentiable from the right, monotone class theorem, time shift operators, progressive measurability, transition probability density, stochastic equivalence, admissible family, tower property, suppose that condition, left limits, filtered probability space, lim sup sup, free propagator, stopping times, multiplicative functional, measurable processes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Urysohn's Lemma New!
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weak fundamental solution, backward propagator, next assertion concerns, stochastic continuity condition, uniform parabolicity condition, final value problem, capacitability theorem, transition probability function, separability set, differentiable from the right, monotone class theorem, time shift operators, progressive measurability, transition probability density, stochastic equivalence, admissible family, tower property, suppose that condition, left limits, filtered probability space, lim sup sup, free propagator, stopping times, multiplicative functional, measurable processes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Urysohn's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 57
books:
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- Evolution Equations (Lecture Notes in Pure and Applied Mathematics) by Gisele Ruiz Goldstein in Back Matter (1), Back Matter (2), and Back Matter (3)
- Differential Equations (with CD-ROM) by Paul Blanchard in Back Matter (1), and Back Matter (2)
- New York (Land of Liberty) by Ellen Sturm in Back Matter (1), and Back Matter (2)
- Parabolic Boundary Value Problems (Operator Theory: Advances and Applications) by Samuil D. Eidelman in Back Matter
- Topology for Analysis by Albert Wilansky in Back Matter
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