StochProc
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This is a basic graduate course on stochastic processes, aimed towards PhD students in applied mathematics and theoretical physics.
The course will consist of three parts: Fundamentals of the theory of stochastic processes, applications (reaction rate theory, surface diffusion....) and non-equilibrium statistical mechanics.
Pavliotis (IC)
StochProc
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3. PART III: NON-EQUILIBRIUM STATISTICAL MECHANICS. Derivation of stochastic differential equations from deterministic dynamics (heat bath models, projection operator techniques etc.). The fluctuation-dissipation theorem. Linear response theory. Derivation of macroscopic equations (hydrodynamics) and calculation of transport coefficients.
The emphasis of the course will be on the presentation of analytical tools that are useful in the study of stochastic models that appear in various problems in applied mathematics, physics, chemistry and biology.
Lectures: Mondays, 10:00-12:00, Huxley 6M42.
Office Hours: By appointment.
Course webpage: /~pavl/stoch_proc.htm
Text: Lecture notes, available from the course webpage. Also, recommended reading from various textbooks/review articles.
Pavliotis (IC)
StochProc
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2. PART II: APPLICATIONS.
Asymptotic problems for the Fokker–Planck equation: overdamped (Smoluchowski) and underdamped (Freidlin-Wentzell) limits. Bistable stochastic systems: escape over a potential barrier, mean first passage time, calculation of escape rates etc. Brownian motion in a periodic potential. Stochastic models of molecular motors. Multiscale problems: averaging and homogenization.
APPLIED STOCHASTIC PROCESSES
G.A. Pavliotis
Department of Mathematics Imperial College London, UK
January 16, 2011
Байду номын сангаас
Pavliotis (IC)
StochProc
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Pavliotis (IC)
StochProc
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1 PART I: FUNDAMENTALS OF CONTINUOUS TIME STOCHASTIC PROCESSES
Elements of probability theory. Stochastic processes: basic definitions, examples. Continuous time Markov processes. Brownian motion Diffusion processes: basic definitions, the generator. Backward Kolmogorov and the Fokker–Planck (forward Kolmogorov) equations. Stochastic differential equations (SDEs); Itô calculus, Itô and Stratonovich stochastic integrals, connection between SDEs and the Fokker–Planck equation. Methods of solution for SDEs and for the Fokker-Planck equation. Ergodic properties and convergence to equilibrium.
The lecture notes are still in progress. Please send me your comments, suggestions and let me know of any typos/errors that you have spotted.
Pavliotis (IC)