Probability Theory Stochastic Processes Notes JNTU – PTSP Notes JNTU of Total Chapter
Please find the download links of Probability Theory Stochastic Processes Notes JNTU | PTSP Notes JNTU are listed below:
Chapter – 1
Probability, measure and integration,Probability spaces and σ-fields,Random variables and their expectation,Convergence of random variables,Independence, weak convergence and uniform integrability.
Chapter – 2
Conditional expectation and Hilbert spaces,Conditional expectation: existence and uniqueness,Hilbert spaces,Properties of the conditional expectation,Regular conditional probability.
Chapter – 3
Stochastic Processes: general theory ,Definition, distribution and versions,Characteristic functions, Gaussian variables and processes,Sample path continuity.
Chapter – 4
Martingales and stopping times,Discrete time martingales and filtrations,Continuous time martingales and right continuous filtrations.Stopping times and the optional stopping theorem,Martingale representations and inequalities , Martingale convergence theorems,Branching processes: extinction probabilities.
Chapter – 5
The Brownian motion,Brownian motion: definition and construction,The reflection principle and Brownian hitting times,Smoothness and variation of the Brownian sample path.
Chapter – 6
Markov, Poisson and Jump processes,Markov chains and processes,Poisson process, Exponential inter-arrivals and order statistics,Markov jump processes, compound Poisson processes.