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Lectures on Diffusion Problems and Partial Differential Equations

Author: S. R. S. Varadhan
Url: http://www.math.tifr.res.in/~publ/ln/tifr64.pdf
Format: Ps, Pdf
Year: 1989
Category: PDE
Pages: 324
Clicks: 951

Contents: The Heat Equation; Kolmogorovís Theorem; The One Dimensional Random Walk; Construction of Wiener Measure: Generalised Brownian Motion; Markov Properties of Brownian Motion; Reflection Principle; Blumenthalís Zero-One Law; Properties of Brownian Motion in One Dimension; Dirichlet Problem and Brownian Motion; Stochastic Integration; Change of Variable Formula; Extension to Vector-Valued Itą Processes;Brownian Motion as a Gaussian Process; Equivalent For of Ito Process; Itoís Formula; Solution of Poissonís Equations; The Feynman-Kac Formula; An Application of the Feynman-Kac Formula.; Brownian Motion with Drift; Integral Equations; Large Deviations; Stochastic Integral for a Wider Class of Functions; Explosions; Construction of a Diffusion Process; Uniqueness of Diffusion Process; On Lipschitz Square Roots; Random Time Changes; Cameron - Martin - Girsanov Formula; Behaviour of Diffusions for Large Times; Invariant Probability Distributions; Ergodic Theorem; Application of Stochastic Integral; Language of Probability; Kolmogorovs Theorem; Martingales; Uniform Integrability; Up Crossings and Down Crossings.

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