Functional Integration and Partial Differential Equations. (AM-109), Volume 109 / / Mark Iosifovich Freidlin

• Autore: Freidlin Mark Iosifovich
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1985
• Descrizione fisica: 1 online resource (557 pages)
• Disciplina: 515.3/53
• Soggetto topico: Differential equations, Partial; Probabilities; Integration, Functional
• Soggetto non controllato: A priori estimate; Absolute continuity; Almost surely; Analytic continuation; Axiom; Big O notation; Boundary (topology); Boundary value problem; Bounded function; Calculation; Cauchy problem; Central limit theorem; Characteristic function (probability theory); Chebyshev's inequality; Coefficient; Comparison theorem; Continuous function (set theory); Continuous function; Convergence of random variables; Cylinder set; Degeneracy (mathematics); Derivative; Differential equation; Differential operator; Diffusion equation; Diffusion process; Dimension (vector space); Direct method in the calculus of variations; Dirichlet boundary condition; Dirichlet problem; Eigenfunction; Eigenvalues and eigenvectors; Elliptic operator; Elliptic partial differential equation; Equation; Existence theorem; Exponential function; Feynman–Kac formula; Fokker–Planck equation; Function space; Functional analysis; Fundamental solution; Gaussian measure; Girsanov theorem; Hessian matrix; Hölder condition; Independence (probability theory); Integral curve; Integral equation; Invariant measure; Iterated logarithm; Itô's lemma; Joint probability distribution; Laplace operator; Laplace's equation; Lebesgue measure; Limit (mathematics); Limit cycle; Limit point; Linear differential equation; Linear map; Lipschitz continuity; Markov chain; Markov process; Markov property; Maximum principle; Mean value theorem; Measure (mathematics); Modulus of continuity; Moment (mathematics); Monotonic function; Navier–Stokes equations; Nonlinear system; Ordinary differential equation; Parameter; Partial differential equation; Periodic function; Poisson kernel; Probabilistic method; Probability space; Probability theory; Probability; Random function; Regularization (mathematics); Schrödinger equation; Self-adjoint operator; Sign (mathematics); Simultaneous equations; Smoothness; State-space representation; Stochastic calculus; Stochastic differential equation; Stochastic; Support (mathematics); Theorem; Theory; Uniqueness theorem; Variable (mathematics); Weak convergence (Hilbert space); Wiener process
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Frontmatter -- CONTENTS -- PREFACE -- INTRODUCTION -- I. STOCHASTIC DIFFERENTIAL EQUATIONS AND RELATED TOPICS -- II. REPRESENTATION OF SOLUTIONS OF DIFFERENTIAL EQUATIONS AS FUNCTIONAL INTEGRALS AND THE STATEMENT OF BOUNDARY V A LU E PROBLEMS -- III. BOUNDARY VALUE PROBLEMS FOR EQUATIONS WITH NON-NEGATIVE CHARACTERISTIC FORM -- IV. SMALL PARAMETER IN SECOND-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS -- V. QUASI-LINEAR PARABOLIC EQUATIONS WITH NON-NEGATIVE CHARACTERISTIC FORM -- VI. QUASI-LINEAR PARABOLIC EQUATIONS WITH SMALL PARAMETER. WAVE FRONTS PROPAGATION -- VII. WAVE FRONT PROPAGATION IN PERIODIC AND RANDOM MEDIA -- LIST OF NOTATIONS -- REFERENCES -- Backmatter
• Sommario/riassunto: This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.
• Titolo autorizzato: Functional Integration and Partial Differential Equations. (AM-109), Volume 109
• ISBN: 1-4008-8159-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154753703321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 109.