Stochastic Processes I -- Lecture 01

Full handwritten lecture notes can be downloaded from here:
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Lecture 1
Introduction
Some examples of stochastic processes 5:55
Formal Definition of a Stochastic Process 23:34
Definition of a Probability Space 26:00
Definition of Sigma-Algebra (or Sigma-Field) 37:29
Definition of a Probability Measure 43:22
Introduction to Uncountable Probability Spaces: The Banach-Tarski Paradoxon 49:15
Definition of Borel-Sigma Field and Lebesgue Measure on Euclidean Space 53:14
Uniform Distribution on a bounded set in Euclidean Space, Example: Uniform Sampling from the unit cube. 1:00:53
Further Examples of countably or uncountable infinite probability spaces: Normal and Poisson distribution 1:03:23
A probability measure on the set of infinite sequences 1:13:46
Definition of Random Variables 1:21:44
Law of a Random Variable 1:25:42 and Examples

[@hayderatrah]

That's exactly what I am looking for, a measure theory approach to stochastic processes. It would be awesome if you can provide us a link of lecture notes of this course.

[@HuyNguyen-fp7oz]

Which textbook used in this course?

[@StephanMescher]

Sehr schön, noch ein RUclipsr an unserem Institut! Frohes Schaffen, auf dass unsere Follower immer freshen Content hier finden! #influencerlife ;-)

[@FreeMarketSwine]

Do you have a list of the topics in each of the videos in the Stochastic Processes playlist?

[@AlexRodriguez-bt5jb]

Hello! Great series! I am wondering if there are lecture notes available to follow along with?

[@fofororo2070]

Thank you professor for this class.

[@RedRainDrop]

example 5: why is the chosen generating set better than omega itself? the index k is fixed?

[@MrBergengruen]

The expansion of a number from [0,1] into the digits of its epansion in negative powers of 2 is a one-to-one map to this set omega. It maps the uniform measure on [0,1] to an i.i.d. sequence of fair Benoulli random variables. If all subsets of sequence space were measurable, then all subsest of [0,1] were (Lebesgue)-measurable, which is not true, c.f. Vitali sets. This shows we need to be careful with the choice of a sigma algebra on sequence space.
In the future, please paste your questions in the forum on the moodle pages of the Univ. of Leipzig so that every one can benefit.