Stochastic Processes

1.	Probability
  1.1    Probabilities of outcomes and events
  1.2    Repetitions and Random variables
  1.3    Conditional probability and independent events
  1.4    Permuatations and combinations
  1.5    Bernouli trials and binomial probabilities
  1.6    Sums and other functions of random variables
  1.7    Averages and expected values of random variables
  1.8    Single Period Inventory
  1.9    Probability calculations

2.	Markov Chains
  2.1   Basic Principles
             2.1.1   The Transition Matrix
             2.1.2   Summary and extensions
             2.1.3   Computations with the Transition Matrix
             2.1.4   Gamblers Ruin and Related Markov Chains
  2.2   The Powers of the Transition Matrix  
             2.2.1   A Formula for the Powers of the Transition Matrix
             2.2.2   Computing the Powers of the Transition Matrix
  2.3   Steady State Probablites   
             2.3.1   Finding Steady State Probabilites
             2.3.2   Computing steady state probabilities
  2.4   Inventory Problems
             2.4.1   Inventory problems
             2.4.2   Inventory problem computations
  2.5   The Time to Reach a State  
             2.5.1   Hitting Times
             2.5.2   Mathematica computations for section 2.5
  2.6   The Probability of Reaching a State 
             2.6.1   Probability of Reaching a State
             2.6.2   Mathematica computations for section 2.6
  2.7   The Number of Visits to a State  
             2.7.1   Number of Visits to a State
             2.7.2   Mathematica computations for section 2.7

3.	Continuous  Probability
  3.1   Continuous probability
  3.2   Joint probability distributions
  3.3   Sums and other functions of random variables
  3.4   Sums of exponential random variables and the Poisson distribution
  3.5   Probability calculations

4.	Continuous Time Markov Processes
  4.1   Basic Principles
  4.2   Markov processes
  4.3   The Chapman-Kolmogoroff equation
  4.4   The Kolmogoroff differential equations
  4.5   Solving Kolmogoroff's Equation - The Matrix Exponential
  4.6   Steady State Probabilities
  4.7   Revenues and costs
  4.8   Markov Process Computations with Mathematica
  4.9   Revenues and costs computations with Mathematica

5.	Queues
  5.1   Single Server Queues
  5.2   Multiple Server Queues
  5.3   Finite Capacity Queues
  5.4   Queueing Networks

6.	Brownian Motion
  6.1   Standard deviations and variances
  6.2   The normal distribution and the central limit theorem
           6.2 (continued)   Gas Velocities - An Example of the normal distribution
  6.3   Diffusion and Brownian Motion
           6.3.2   Brownian motion computations
  6.4   Geometric Brownian motion
           6.4.2   Geometric Brownian motion computations
  6.5   Pricing Stock Options
           6.5.2   Stock option computations
  6.6   Reflected Brownian motion
  6.7   Absorbed Brownian motion  
  
7.	Renewal Theory and Machine Replacement
  7.1   Renewal theory & machine replacement
  
     Bibliography

     An Introduction to Mathematica

  Mathematics 420/520 Directory