Are you looking for the best Probability With Martingales? Based on expert reviews, we ranked them. We've listed our top-ranked picks, including the top-selling Probability With Martingales.
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- Williams, David (Author)
- English (Publication Language)
- 251 Pages - 02/22/1991 (Publication Date) - Cambridge University Press (Publisher)
- Schilling, René L. (Author)
- English (Publication Language)
- 490 Pages - 04/03/2017 (Publication Date) - Cambridge University Press (Publisher)
- Amazon Kindle Edition
- Mosteller, Frederick (Author)
- English (Publication Language)
- 100 Pages - 04/26/2012 (Publication Date) - Dover Publications (Publisher)
- Used Book in Good Condition
- Hardcover Book
- Chow, Yuan Shih (Author)
- English (Publication Language)
- 511 Pages - 09/11/1997 (Publication Date) - Springer (Publisher)
- Pull out a block without crashing the stack to win at Jenga
- Includes 54 Jenga hardwood blocks, stacking sleeve with instructions
- Simple, solid, and timeless
- It takes skill, strategy, and luck. Challenge yourself or play with friends
- Win by being the last player to remove a block without causing the stack to crash
- Hardcover Book
- Durrett, Rick (Author)
- English (Publication Language)
- 430 Pages - 05/30/2019 (Publication Date) - Cambridge University Press (Publisher)
- Amazon Kindle Edition
- Ross, Sheldon M. (Author)
- English (Publication Language)
- 823 Pages - 03/09/2019 (Publication Date) - Academic Press (Publisher)
- Hardcover Book
- Bhattacharya, Rabi (Author)
- English (Publication Language)
- 411 Pages - 09/21/2021 (Publication Date) - Springer (Publisher)
- Amazon Kindle Edition
- Shiryaev, Albert N. (Author)
- English (Publication Language)
- 503 Pages - 07/08/2016 (Publication Date) - Springer (Publisher)
- 【Basic information】: Stroke adjustable 30-150mm. Rated Voltage: DC 24V. No load maximum Speed:120RPM. Pushing Force: 1.5-7.5kg.
- 【Stroke Adjustable】: The stroke can be adjusted by changing the position of the screw on the slide rail. The stroke of this product can be...
- 【Fixing Holes】: The aluminum alloy bracket provides 3 fixing holes for easy installation. It is 8mm.
- 【Aluminum Alloy Material】: The surface has been polished 27 times, and the structure is tightly designed.
- 【With Remote Controller】Remote control distance up to 10 meters in an open environment. You can control the motor in a distance more easily.
- Meet Echo Dot Kids - Our most popular smart speaker with Alexa, made for kids (not a toy). The super-fun design delivers crisp vocals and balanced...
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- Amazon Kindle Edition
- Durrett, Richard (Author)
- English (Publication Language)
- 339 Pages - 03/29/2018 (Publication Date) - CRC Press (Publisher)
- Schilling, René L. (Author)
- English (Publication Language)
- 448 Pages - 02/02/2021 (Publication Date) - Independently published (Publisher)
- Hardcover Book
- Kallenberg, Olav (Author)
- English (Publication Language)
- 958 Pages - 02/08/2021 (Publication Date) - Springer (Publisher)
- Amazon Kindle Edition
- Dobrow, Robert P. (Author)
- English (Publication Language)
- 435 Pages - 03/29/2016 (Publication Date) - Wiley (Publisher)
- NEW - SUPER MEGA LUCKY BOX 2021 - The Latest Creation Pulled from the Mind of the Gameplay Wizard & Inventor of "Sushi Go!", Phil Walker-Harding
- Gameplay Reimagined: SUPER MEGA LUCKY BOX was Creatively Designed for Fun, Not Size. Excellent for Single, Multi up to Large Group Play!
- Box Contents: (60) Lucky Box Cards, (30) Lightning Tokens, (24) Moon Tokens, (18) Number Cards (Two Sets of 1-9), (6) Super Mega Scorecards, (6) Dry...
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- Hardcover Book
- Winters-Hilt, Stephen (Author)
- English (Publication Language)
- 592 Pages - 01/06/2022 (Publication Date) - Wiley (Publisher)
- Hardcover Book
- Musiela, Marek (Author)
- English (Publication Language)
- 636 Pages - 11/25/2004 (Publication Date) - Springer (Publisher)
- Klenke, Achim (Author)
- English (Publication Language)
- 730 Pages - 10/31/2020 (Publication Date) - Springer (Publisher)
- Stoyanov, Jordan M. (Author)
- English (Publication Language)
- 400 Pages - 01/15/2014 (Publication Date) - Dover Publications (Publisher)
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FAQ:
Q: How do you find the probability of a martingale?
A: Let X t+1 = X t ± b t where +b t and -b t occur with equal probability b t is measurable ℱ t, and the outcome ±b t is measurable ℱ t+1 (in other words, my “bet” b t can only depend on what has happened so far and not on the future, but my knowledge ℱ t includes the outcome of all past bets). Then {X t |ℱ t } is a martingale.
Q: Is the discrete time martingale a one semester course?
A: The primary focus of the book is discrete time martingales as is obvious from its title, and so it isn’t a complete one semester course (topics which don’t make a mention are infinitely divisible laws, ergodic theory, markov chains, convergence in probability measures to name a few), but neither does it aim to be.
Q: What are the useful properties of martingales?
A: The useful property of martingales is that we can verify the martingale property locally, by proving either that E [X t+1 |ℱ t] = X t or equivalently that E [X t+1 – X t |ℱ t] = E [X t+1 |ℱ t] – X t = 0. But this local property has strong consequences that apply across long intervals of time, as we will see below.
Q: How to show that y t is a martingale?
A: To show that Y t is a martingale, compute E [Y t+1 |ℱ t] = E [X t+1 -Z t+1 |ℱ t] = E [X t+1 -E [X t+1 -X t |ℱ t ]|ℱ t] = E [X t+1 -X t+1 +X t |ℱ t] = X t. For supermartingales, the same decomposition works, but now Z t is non-increasing.