Stochastic Processes
Academic (University) preparation with worked examples, written practice and independent learning assessments.
Independent university-level study of Stochastic Processes. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Process definitions; Finite-dimensional distributions; Stationarity; Sample paths. Discrete Markov chains; Transition matrices; Recurrence; Invariant distributions. Poisson processes; Exponential waiting times; Thinning; Superposition. Continuous-time chains; Generators; Birth-death models; Kolmogorov equations. Martingales; Stopping times; Optional stopping; Convergence. Brownian motion; Gaussian increments; Scaling; Reflection principle. Stochastic integration; Ito formula; Stochastic differential equations; Diffusion models. Queues; Renewal theory; Simulation diagnostics; Stochastic modeling project. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.
Curriculum
One complete track with its own final exam and certificate.
Independent university-level study of Stochastic Processes. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Process definitions; Finite-dimensional distributions; Stationarity; Sample paths. Discrete Markov chains; Transition matrices; Recurrence; Invariant distributions. Poisson processes; Exponential waiting times; Thinning; Superposition. Continuous-time chains; Generators; Birth-death models; Kolmogorov equations. Martingales; Stopping times; Optional stopping; Convergence. Brownian motion; Gaussian increments; Scaling; Reflection principle. Stochastic integration; Ito formula; Stochastic differential equations; Diffusion models. Queues; Renewal theory; Simulation diagnostics; Stochastic modeling project. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required.
Process definitions; Finite-dimensional distributions; Stationarity; Sample paths
- Foundations of Stochastic Processes: Definitions, Probability Spaces, and State Spaces Lab60 min
- Finite-Dimensional Distributions and the Kolmogorov Extension Theorem Lab60 min
- Stationarity: Strict Stationarity, Wide-Sense Stationarity, and Ergodicity Lab60 min
- Sample Path Properties: Modifications, Indistinguishability, and Regularity Lab60 min