Stochastic models | Statistical data types | Stochastic processes
In probability theory and related fields, a stochastic (/stoʊˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries. The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects. Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications. (Wikipedia).
Basic stochastic simulation b: Stochastic simulation algorithm
(C) 2012-2013 David Liao (lookatphysics.com) CC-BY-SA Specify system Determine duration until next event Exponentially distributed waiting times Determine what kind of reaction next event will be For more information, please search the internet for "stochastic simulation algorithm" or "kin
From playlist Probability, statistics, and stochastic processes
MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu
From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
Hybrid sparse stochastic processes and the resolution of (...) - Unser - Workshop 2 - CEB T1 2019
Michael Unser (EPFL) / 12.03.2019 Hybrid sparse stochastic processes and the resolution of linear inverse problems. Sparse stochastic processes are continuous-domain processes that are specified as solutions of linear stochastic differential equations driven by white Lévy noise. These p
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From playlist Research
Understanding Discrete Event Simulation, Part 3: Leveraging Stochastic Processes
Watch more MATLAB Tech Talks: https://goo.gl/ktpVB7 Free MATLAB Trial: https://goo.gl/yXuXnS Request a Quote: https://goo.gl/wNKDSg Contact Us: https://goo.gl/RjJAkE Learn how discrete-event simulation uses stochastic processes, in which aspects of a system are randomized, in this MATLAB®
From playlist Understanding Discrete-Event Simulation - MATLAB Tech Talks
Jana Cslovjecsek: Efficient algorithms for multistage stochastic integer programming using proximity
We consider the problem of solving integer programs of the form min {c^T x : Ax = b; x geq 0}, where A is a multistage stochastic matrix. We give an algorithm that solves this problem in fixed-parameter time f(d; ||A||_infty) n log^O(2d) n, where f is a computable function, d is the treed
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Ngoc Mai Tran: Stochastic geometry to generalize the Mondrian process
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We consider a Bayesian sequential experimentation problem. We identify environments in which the average number of experiments that is conducted per unit of time is large and the informativeness of each individual experiment is low. Under such regimes, we derive a diffusion approximation f
From playlist Thematic Program on Stochastic Modeling: A Focus on Pricing & Revenue Management
Prob & Stats - Markov Chains (8 of 38) What is a Stochastic Matrix?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a stochastic matrix. Next video in the Markov Chains series: http://youtu.be/YMUwWV1IGdk
From playlist iLecturesOnline: Probability & Stats 3: Markov Chains & Stochastic Processes
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PROGRAM : BANGALORE SCHOOL ON STATISTICAL PHYSICS - XII (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, Bengaluru) and Sanjib Sabhapandit (RRI, Bengaluru) DATE : 28 June 2021 to 09 July 2021 VENUE : Online Due to the ongoing COVID-19 pandemic, the school will be conducted through online
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From playlist Quantitative Finance Seminar @ SNS
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PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
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Stilian Stoev: Function valued random fields: tangents, intrinsic stationarity, self-similarity
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From playlist Probability and Statistics
Martin Schweizer: Some stochastic Fubini theorems
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 Analysis and its Applications
Stochastic processes by VijayKumar Krishnamurthy
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Stochastic Description of Noisy Open Quantum Systems by Tony Jin
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
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Winter School on Quantitative Systems Biology DATE:04 December 2017 to 22 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Winter S
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