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Course Objectives The course aims to give an introduction to the theory of stochastic processes with special emphasis on applications and examples. Course Content Stochastic Processes: definition, finite dimensional distributions, stationarity, sample path spaces, construction, examples Filtrations, stopping times, conditional expectation. Markov processes: definition, main properties and examples. Birth and death processes. Poisson process with applications on queueing models.
- ST Stochastic Processes.
- Schedule, syllabus and examination date!
- Organization of the lecture.
Martingales: definition, main properties and examples. Brownian motion: definition, construction and main properties. Ito integral and stochastic differential equations. Applications and examples. Stochastic Processes in Physics and Chemistry 3rd edn Amsterdam, Delorme, M. Maximum of a fractional Brownian motion: analytic results from perturbation theory.
Perturbative expansion for the maximum of fractional Brownian motion. E 94 , Masoliver, J. First-passage times for non-Markovian processes: correlated impacts on a free process. A 34 , Burkhardt, T. Semiflexible polymer in the half plane and statistics of the integral of a Brownian curve. On the one-sided exit problem for fractional Brownian motion.
Recent Stochastic Processes and their Applications Articles
Sanders, L. First passage times for a tracer particle in single file diffusion and fractional Brownian motion.
Mean first-passage times of non-Markovian random walkers in confinement. Nature , — DeGennes, P. Kinetics of diffusion-controlled processes in dense polymer systems. Non-entangled regimes. Diffusion and Reactions in Fractals and Disordered Systems. Hughes, B. Grabner, P. Their Appl. Asymptotics of the transition probabilities of the simple random walk on self-similar graphs.
Stochastic Processes: Data Analysis and Computer Simulation
Soc , — Weber, S. Random walks on Sierpinski gaskets of different dimensions. E 82 , Zero constant formula for first-passage observables in bounded domains. Chechkin, A. Tejedor, V. Theor 44 , Blumenthal, R. On the distribution of first hits for the symmetric stable processes.
Soc 99 , — Levernier, N. Universal first-passage statistics in aging media. E 98 , Molchan, G. Maximum of a fractional Brownian motion: probabilities of small values. Krug, J. Persistence exponents for fluctuating interfaces.
STK – Modelling by Stochastic Processes - University of Oslo
E 56 , — Grimm, M. Brownian motion in a maxwell fluid. Soft Matter 7 , — Turiv, T. Effect of collective molecular reorientations on Brownian motion of colloids in nematic liquid crystal. Science , — Ochab-Marcinek, A. Scale-dependent diffusion of spheres in solutions of flexible and rigid polymers: mean square displacement and autocorrelation function for FCS and DLS measurements. Mandelbrot, B.
Noah, Joseph, and operational hydrology. Water Resour. Cutland, N. Ernst, D. Fractional Brownian motion in crowded fluids. Soft Matter 8 , — Burnecki, K. Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion. Malakar, K. Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension.
Solution manual. Xtra exercises.
Errata for the book. Maria Sandsten.
- Review ARTICLE.
- MATH Stochastic Processes | School of Mathematics and Statistics;
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News HT Webpage for ! The exam is corrected and can be viewed Monday November 26 More typos by a confused 'tryckfelsnisse'.
Please check the solution of 5c in old exam Tue Oct 30 Thu Nov 1 Course contents Stochastic processes find applications in a wide variety of fields and offer a refined and powerful framework to examine and analyse time series. Week 1: September 3 - September 7 2. Week 7: October 15 — October 19 Review and old exams, see below. Thu Sept 13 8.
Thu Sept 20 8. Thu Sept 27 8.