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  2. Martingale (collar) - Wikipedia

    en.wikipedia.org/wiki/Martingale_(collar)

    Martingale dog collars are also known as greyhound, whippet or humane choke collars. The martingale dog collar was designed for sighthounds because their necks are larger than their heads and they can often slip out of buckle collars. These collars have gained popularity among owners of other breeds in the recent past with many trainers now ...

  3. Martingale (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Martingale_(probability...

    In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. Stopped Brownian motion is an example of a martingale. It can model an even coin-toss ...

  4. Martingale - Wikipedia

    en.wikipedia.org/wiki/Martingale

    Martingale (collar) for dogs and other animals; Martingale (betting system), in 18th century France; a dolphin striker, a spar aboard a sailing ship; In the sport of fencing, a martingale is a strap attached to the sword handle to prevent a sword from being dropped if disarmed; In the theatrical lighting industry, martingale is an obsolete term ...

  5. Optional stopping theorem - Wikipedia

    en.wikipedia.org/wiki/Optional_stopping_theorem

    Now consider a random walk X that starts at 0 and stops if it reaches –m or +m, and use the Y n = X n 2 – n martingale from the examples section. If τ is the time at which X first reaches ±m, then 0 = E[Y 0] = E[Y τ] = m 2 – E[τ]. This gives E[τ] = m 2. Care must be taken, however, to ensure that one of the conditions of the theorem ...

  6. Local martingale - Wikipedia

    en.wikipedia.org/wiki/Local_martingale

    In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; in particular, every local martingale that is bounded from below is a supermartingale, and every local martingale that is bounded from above is a submartingale; however, a local ...

  7. Trainer explains how to get your pup to behave well (and it's ...

    www.aol.com/trainer-explains-pup-behave-well...

    Training dogs with treats can be easier than you might think, and this is just one example. This isn’t only limited to puppies, either. “Capturing desirable behaviors is not a technique that ...

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