Stochastic process online course

Free Online Course Passist Certificate Available 12 weeks lengthy 2ninth Jul, 2019 22nd Jan, 2018 2third Jan, 2017

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This course explanations and expositions of stochastic procedures concepts which they need for their experiments and research. It additionally covers theoretical ideas pertaining to taking care of various stochastic modeling. This course provides classification and also properties of stochastic processes, discrete and consistent time Markov chains, simple Markovian queueing models, applications of CTMC, martingales, Brownian movement, renewal procedures, branching processes, stationary and also autoregressive processes.INTENDED AUDIENCE: Under-graduate, Post-graduate and also PhD students of math, electric engineering, computer engineeringPRE REQUISITES : A fundamental course on ProbabilityINDUSTRY SUPPORT: Goldman Sachs, FinMachenics, Deutsche Bank and also other finance providers.

COURSE LAYOUT

Week 1:Probcapacity concept refresherReview to stochastic processOverview to stochastic process (contd.)Week 2:Probcapacity theory refresher (contd.)Problems in random variables and also distributionsProblems in Sequence of random variablesWeek 3:Definition and also simple stochastic processDefinition, classification and ExamplesSimple stochastic processesWeek 4:Discrete-time Markov chainsIntroduction, Definition and also Transition Probcapacity MatrixChapman-Kolmogorov EquationsGroup of States and also Limiting DistributionsWeek 5:Discrete-time Markov chains (contd.)Limiting and also Stationary DistributionsLimiting Distributions, Ergodicity and also stationary distributionsTime Reversible Markov Chain, Application of Irreducible Markov chains in Queueing ModelsReducible Markov ChainsWeek 6:Continuous-time Markov chainsDefinition, Kolmogrov Differential Equation and Infinitesimal Generator MatrixLimiting and also Stationary Distributions, Birth Death ProcessesPoisboy processesWeek 7:Continuous-time Markov Chains (contd.)M/M/1 Queueing modelSimple Markovian Queueing ModelsWeek 8:Applications of CTMCQueueing networksCommunication systemsStochastic Petri NetsWeek 9:MartingalesConditional Expectation and filterationDefinition and also straightforward examplesWeek 10:Brownian MotionDefinition and PropertiesProcesses Derived from Brownian MotionStochastic Differential EquationWeek 11:Renewal ProcessesRenewal Function and also EquationGeneralized Renewal Processes and also Renewal Limit TheoremsMarkov Renewal and Markov Regenerative ProcessesNon Markovian QueuesApplication of Markov Regenerative ProcessesWeek 12:Branching Processes, Stationary and also Autoregressive Processes