- 0
- 12 weeks long
- Swayam
- English
Course Overview
This course explanations and expositions of stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts pertaining to handling various stochastic modeling. This course provides classification and properties of stochastic processes, discrete and continuous time Markov chains, simple Markovian queueing models, applications of CTMC, martingales, Brownian motion, renewal processes, branching processes, stationary and autoregressive processes.
INTENDED AUDIENCE: Under-graduate, Post-graduate and PhD students of mathematics, electrical engineering, computer engineeringPRE REQUISITES : A basic course on ProbabilityINDUSTRY SUPPORT: Goldman Sachs, FinMachenics, Deutsche Bank and other finance companies.
Course Circullum
COURSE LAYOUT
Week 1:Probability theory refresher- Introduction to stochastic process
- Introduction to stochastic process (contd.)
- Problems in random variables and distributions
- Problems in Sequence of random variables
- Definition, classification and Examples
- Simple stochastic processes
- Introduction, Definition and Transition Probability Matrix
- Chapman-Kolmogorov Equations
- Classification of States and Limiting Distributions
- Limiting and Stationary Distributions
- Limiting Distributions, Ergodicity and stationary distributions
- Time Reversible Markov Chain, Application of Irreducible Markov chains in Queueing Models
- Reducible Markov Chains
- Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix
- Limiting and Stationary Distributions, Birth Death Processes
- Poisson processes
- M/M/1 Queueing model
- Simple Markovian Queueing Models
- Queueing networks
- Communication systems
- Stochastic Petri Nets
- Conditional Expectation and filteration
- Definition and simple examples
- Definition and Properties
- Processes Derived from Brownian Motion
- Stochastic Differential Equation
- Renewal Function and Equation
- Generalized Renewal Processes and Renewal Limit Theorems
- Markov Renewal and Markov Regenerative Processes
- Non Markovian Queues
- Application of Markov Regenerative Processes
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This Course Include:
COURSE LAYOUT
Week 1:Probability theory refresher- Introduction to stochastic process
- Introduction to stochastic process (contd.)
- Problems in random variables and distributions
- Problems in Sequence of random variables
- Definition, classification and Examples
- Simple stochastic processes
- Introduction, Definition and Transition Probability Matrix
- Chapman-Kolmogorov Equations
- Classification of States and Limiting Distributions
- Limiting and Stationary Distributions
- Limiting Distributions, Ergodicity and stationary distributions
- Time Reversible Markov Chain, Application of Irreducible Markov chains in Queueing Models
- Reducible Markov Chains
- Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix
- Limiting and Stationary Distributions, Birth Death Processes
- Poisson processes
- M/M/1 Queueing model
- Simple Markovian Queueing Models
- Queueing networks
- Communication systems
- Stochastic Petri Nets
- Conditional Expectation and filteration
- Definition and simple examples
- Definition and Properties
- Processes Derived from Brownian Motion
- Stochastic Differential Equation
- Renewal Function and Equation
- Generalized Renewal Processes and Renewal Limit Theorems
- Markov Renewal and Markov Regenerative Processes
- Non Markovian Queues
- Application of Markov Regenerative Processes
- Provider:Swayam
- Certificate:Paid Certificate Available
- Language:English
- Duration:12 weeks long
- Language CC: