- DYNAMICS OF CURRENT-BASED, POISSON DRIVEN, INTEGRATE-AND-FIRE NEURONAL NETWORKS
- ERROR ANALYSIS OF A STOCHASTIC IMMERSED BOUNDARY METHOD INCORPORATING THERMAL FLUCTUATIONS
- Proceedings in Applied Mathematics and Mechanics, 31 October 2007 Method of Multiple Scales with Three Time Scales
- A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic
- Subdiffusion and Superdiffusion in Lagrangian Stochastic Models of Oceanic Transport
- Incorporating Thermal Fluctuations into the Immersed Boundary Method
- Two Different Rapid Decorrelation in Time Limits for Turbulent Diffusion
- A Review of Some Monte Carlo Simulation Methods for Turbulent Systems
- Introduction to Probability: Problem Solutions
- THE PDF APPROACH TO TURBULENT POLYDISPERSED TWO-PHASE FLOWS
- Lectures on Turbulent Diffusion (A. J. Majda and P. R. Kramer), Spring 2005 137 Appendix 2.C Conditional Probability and Expectation
- Denis Talay 63 3.Simulation of Stochastic Di erential Systems
- Financial Derivatives and Partial Differential Equations Author(s): Robert Almgren
- Lectures on Turbulent Diffusion (A. J. Majda and P. R. Kramer), Spring 2005 64 1.2 Steady Linear Mean Flow Model without Molecular Dif-
- Lectures on Turbulent Diffusion (A. J. Majda and P. R. Kramer), Spring 2005 30 Throughout the lectures, we offer the reader some exercises and some open-ended
- Proceedings in Applied Mathematics and Mechanics, 17 October 2007 Stochastic Immersed Boundary Method Incorporating Thermal Fluctua-
- NL3284 FokkerPlanck equation 1 NL3284 FokkerPlanck equation
- TWO COARSE-GRAINING STUDIES OF STOCHASTIC MODELS IN MOLECULAR BIOLOGY
- NL3281 Brownian motion 1 NL3281 Brownian motion
- HOMOGENIZATION THEORY FOR A REPLENISHING PASSIVE SCALAR FIELD
- Proceedings in Applied Mathematics and Mechanics, 31 October 2007 Effective transport properties for flashing ratchets using homogenization
- STOCHASTIC MODE REDUCTION FOR THE IMMERSED BOUNDARY METHOD
- STOCHASTIC MODE REDUCTION FOR PARTICLE-BASED SIMULATION METHODS FOR COMPLEX MICROFLUID SYSTEMS
- Simpli ed Models for Turbulent Di usion: Theory, Numerical Modelling, and Physical
- PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS
- Homogenization and mixing measures for a replenishing passive scalar field
- Brownian motion vanishes only as the square root of the time elapsed. Consequently, the differential equation describing the tracer trajectories (or more formally the characteristics
- Cascade-Induced Synchrony in Stochastically-Driven Neuronal Networks Katherine A. Newhall,1
- Lectures on Turbulent Diffusion (A. J. Majda and P. R. Kramer), Spring 2005 48 Here, we rewrote the square of the integral in terms of polar coordinates in the (x1, x2)
- It versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise
- Closure Approximations for Passive Scalar Turbulence
- Proceedings in Applied Mathematics and Mechanics, 31 October 2007 Parametrization for Mesoscale Ocean Transport through Random Flow
- SIAM REVIEW c 2001 Society for Industrial and Applied Mathematics Vol. 43, No. 3, pp. 525546
- Comparative Analysis of Multiscale Gaussian Random Field Simulation Algorithms
- On the Foundations of the Stochastic Immersed Boundary Method
- Diagnosing lateral mixing in the upper ocean with virtual tracers: Spatial and temporal
- Theoretical Framework for Microscopic Osmotic Phenomena Theoretical Framework for Microscopic Osmotic Phenomena
- A Local Kinetic Interpretation of Entropy Production through Reversed Diffusion A. Porporato
- Homework 1 posted, due Friday, September 30, 2 PM. Independence of random variables
- Continuing the calculation of the absorption probability for a branching process.
- Homework 3 due Tuesday, November 29 The derivation of the Kolmogorov backward equation from
- Homework 4 due Thursday, December 15 at 5 PM. Hard Final exam is on Wednesday, December 14 at 3 PM. If you want
- Homework 1 due Friday, September 30 at 2 PM. Office hours on 09/28: Only 11 AM-12 PM (not at 3 PM)
- Karlin & Taylor Chs. 2 & 3 Resnick Ch. 1
- Continuing the discussion of long-time behavior of countable-state Markov chains from last time, we now turn to transient communication classes.
- Homework 4 due on Thursday, December 15 at 5 PM (hard deadline). How are formulas for large-time behavior of discrete-time Markov chains
- I will post Homework 1 soon, probably over the weekend, due Friday, September 30.
- No class next week. No office hours either. Next class will be 11/01.
- The main reference is Resnick Secs. 2.12-2.15, which extends to countably infinite Markov chains as well as finite Markov chains.
- Office hours: Wednesdays 11 AM-12 PM (this class preference), Mondays 2 PM -3 PM (free-for-all),
- Homework 2 posted, due Tuesday, October 18 Math Colloquium on Tuesday, October 11, 4 PM, Amos Eaton 214
- Reading: Lawler Ch. 1 All homework 1 has been graded; pick up during office hours.
- Stochastic Pulse Switching in a Degenerate Resonant Optical Medium Ethan P. Atkins,1
- First an addendum to generating functions. They can also be used to compute the probability distribution for
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- Note special talk on mathematics and music, Wednesday, October 5 at 2 PM at EMPAC.
- Asymptotic Analysis of Microtubule-Based Transport by Multiple Identical Molecular Motors
- The fundamental object describing the dynamics of a CTMC (continuous-time Markov chain) is the
- When you do direct (Monte Carlo) simulations of a Markov chain, then the quality of the answers that you get from taking statistical averages
- Reference: Karlin and Taylor, Sec. 5.9 Homework 3 is due Tuesday, November 29 at 2 PM
- Homework 3 posted, due Tuesday, November 29. Continuing with our classification of birth-death chains on
- Stochastic processes entails a dynamical approach to probability theory, with uncertainty entering a system over time.
- Randomized Spectral and Fourier-Wavelet Methods for Multidimensional Gaussian Random Vector Fields 6