Together with Prof. Benjamin Friedrich, I am turning the notes of his lecture on ‘Stochastic Processes’ into a book. It’s intended for first-year Master’s students in biophysics.
I will publish the book progressively on The Planet. Feel free to subscribe and follow our progress.
The preliminary outline is here:
1 Prerequisites from Probability Theory
1.1 Mathematical Foundations
1.2 Probability in Physics
1.3 Important Probability Distributions
1.4 The Central-Limit Theorem
1.5 Stochastic Processes
2 Diffusion & Random Walk
2.1 Random Walker
2.2 Continuum Limit: Diffusion Equation
2.3 Random Force Model
3 Langevin Equation and Fokker-Planck Equation
3.1 Langevin Equation
3.2 Fokker-Planck-Equation
3.3 Master Equation
4 Dynkin Equation
4.1 Mean First-Passage Times and Dynkin Equation
4.2 Kramers Escape Rate Theory
4.3 Diffusion to Capture
4.4 Polya’s Theorem
5 Active Oscillators and Synchronization
5.1 Van-der-Pol Oscillator
5.2 Hopf-Oscillator with Noise
5.3 Two Coupled Phase Oscillators
5.4 Synchronization in the Presence of Noise
6 Stochastic Resonance
7 Ito- versus Stratonovich Calculus
7.1 Numerical Motivation
7.2 Different Interpretations
7.3 Rotational Diffusion in 3D
7.4 How to derive a correct Langevin equation?
7.5 Numerical Integration of nonlinear SDE
8 Fluctuation-Dissipation-Theorem (FDT)
8.1 Historical Examples
8.2 FDT for Classical Systems
9 A Link to Statistical Physics
9.1 Detailed Balance
9.2 Increase of Relative Entropy
9.3 Equilibrium vs. Non-Equilibrium
9.4 Thermal Fluctuations: Space-dependent Diffusion
9.5 Entropy Production
10 Decision Theory
10.1 StatisticalTesting
10.2 Student’s t-Test
10.3 Fischer’s Exact: Testing Categorial Data for Correlations
10.4 Estimation Theory
10.5 Kalman Filters