# Introduction to Brownian Motion , Lecture Notes - Mathematics

Introduction to Brownian Motion, Basic Properties, The Finite-Dimensional Distributions of BM, Conditional Densities, Hitting Times and The Refection Principle, Using Martingales

# Continuous Time Markov Chains , Lecture Notes - Mathematics

Continuous-Time Markov Chains, Problems for Discussion and Solutions, Rate Diagram

# Exponential Distribution , Lecture Notes - Mathematics

Competing Clocks with Exponential Timers, DTMC with Poisson Transitions, Limiting Probabilities, Birth-and-Death Processes, Reverse-Time, CTMC's and Reversibility, Time-Dependent Transition Probabilities, Issues

# Continuous Time Markov Chains , Lecture Notes - Mathematics

Continuous-Time Markov Chains, Problems for Discussion and Solutions, Rate Diagram

# Exponential Distribution , Lecture Notes - Mathematics

Competing Clocks with Exponential Timers, DTMC with Poisson Transitions, Limiting Probabilities, Birth-and-Death Processes, Reverse-Time, CTMC's and Reversibility, Time-Dependent Transition Probabilities, Issues

# Markov Chains Introduction to Stochastic Model, Lecture Notes - Mathematics

Markov Chains, Introduction to Stochastic Model, The Inspection Paradox, Renewal Reward theory, Exercises

# Introduction to Brownian Motion , Lecture Notes - Mathematics

Introduction to Brownian Motion, Basic Properties, The Finite-Dimensional Distributions of BM, Conditional Densities, Hitting Times and The Refection Principle, Using Martingales

# Markov Chain Example in Credit Risk Modelling , Lecture Notes - Mathematics

A Markov Chain Example in Credit Risk Modelling

# Markov Chains Introduction to Stochastic Model, Lecture Notes - Mathematics

Markov Chains, Introduction to Stochastic Model, The Inspection Paradox, Renewal Reward theory, Exercises

# Markov Chains Introduction to Renewal Theory, Lecture Notes - Mathematics

Markov Chains, Introduction to Renewal Theory, Formalizing what has been assumed, Random variables and stochastic processes, Enter renewal processes, Supporting Theory

# Markov Chains Extension 2, Lecture Notes - Mathematics

Markov Chains Extension, The insurance example, Exercises

# Markov Chains Extension 1, Lecture Notes - Mathematics

Even More on Markov Chains, Exercises

# Markov Chains Contraction Approach , Lecture Notes - Mathematics

Markov Chains Contraction Approach, The limit for aperiodic irreducible finite-state DTMC's, Finding the appropriate norm