In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale. A stochastic series X is an MDS if its expectation with respect to the past is zero. Formally, consider an adapted sequence on a probability space . is an MDS if it satisfies the following two conditions: , and, for all . By construction, this implies that if is a martingale, then will be an MDS—hence the name. The MDS is an extremely useful construct in modern probability theory because it implies much milder restrictions on the memory of the sequence than independence, yet most limit theorems that hold for an independent sequence will also hold for an MDS. A special case of MDS, denoted as {Xt,t}0 is known as innovative sequence of Sn; where Sn and are corresponding to random walk and filteration of the random processes . In probability theory innovation series is used to emphasize the generality of Doob representation. In signal processing the innovation series is used to introduce Kalman filter. The main differences of innovationterminologies are in the applications. The later application aims to introduce the nuance of samples to the model by random sampling. (Wikipedia).
This video introduces the Fibonacci sequence and provides several examples of where the Fibonacci sequence appear in nature. http:mathispower4u.com
From playlist Mathematics General Interest
What is the difference between finite and infinite sequences
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
B24 Introduction to the Bernoulli Equation
The Bernoulli equation follows from a linear equation in standard form.
From playlist Differential Equations
What is the alternate in sign sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
5 4 Stochastic integral Part 2
BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology
From playlist BEM1105x Course - Prof. Jakša Cvitanić
C56 Continuation of previous problem
Adding a bit more depth to the previous problem.
From playlist Differential Equations
15. Graph limits II: regularity and counting
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains how graph limits can be used to gener
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
This video introduces sequences. http://mathispower4u.yolasite.com/
From playlist Infinite Series
FinMath L2-1: The general Ito integral
Welcome to the second lesson of Financial Mathematics! This is a course I teach in the master in applied mathematics of Delft University of Technology. I simply record my live classes to be shared online. I make use of my own lecture notes. The first chapter, which we are using in the v
From playlist Financial Mathematics
David Kelly: Fast slow systems with chaotic noise
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics
Xu Zhendong - From the Littlewood-Paley-Stein Inequality to the Burkholder-Gundy Inequality
We solve a question asked by Xu about the order of optimal constants in the Littlewood-Paley-Stein inequality. This relies on a construction of a special diffusion semi-group associated with a martingale which relates the Littlewood G-function with the martingale square function pointwise.
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
16. Graph limits III: compactness and applications
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Continuing the discussion of graph limits, Prof. Zhao pro
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
24. Martingales: Stopping and Converging
MIT 6.262 Discrete Stochastic Processes, Spring 2011 View the complete course: http://ocw.mit.edu/6-262S11 Instructor: Robert Gallager License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.262 Discrete Stochastic Processes, Spring 2011
Léonard Cadilhac - Non-commutative Pointwise Ergodic Theorem for Actions of Amenable Groups
Birkhoff's famous theorem asserts the pointwise convergence of ergodic averages associated with a measure preserving transformation of a measure space. In this talk, I will discuss generalizations of this theorem in two directions: the transformation will be replaced by the action of an am
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Marie-Claire Quenez: European and american optionsin a non-linear incomplete market with default
HYBRID EVENT Recorded during the meeting "Advances in Stochastic Control and Optimal Stopping with Applications in Economics and Finance" the September 12, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video a
From playlist Probability and Statistics
Daniel Balint: Discounting invariant FTAP for large financial markets
Abstract: For large financial markets as introduced in Kramkov and Kabanov 94, there are several existing absence-of-arbitrage conditions in the literature. They all have in common that they depend in a crucial way on the discounting factor. We introduce a new concept, generalizing NAA1 (K
From playlist Probability and Statistics
Introduction To Sequences | Algebra | Maths | FuseSchool
In this video we’re going to discover some key sequences terminology and how to recognise and generate some important sequences. We will come across all of these key sequences... Arithmetic, Linear, Triangular, Square, Cube, Fibonacci, Quadratic, Geometric. And these key words; Term, 1st t
From playlist MATHS