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      A stochastic process is a collection of random variables usually indexed by a totally ordered set.

      3
      votes
      2answers
      Consider general Brownian bridge W(0)=0; W(T) = a. (Here "general" means: $W(T)\ne 0$). What is the probability W(t) >= b, for all $ t \in [0, T] $ ? Is there close simple formula in terms of a …
      asked May 5 '17 by Alexander Chervov
      3
      votes
      1answer
      Setup. Let casisno generate a color: black or red with equal probability. Let client try to guess the color. If guess is correct - he earns 1 coin from casino, if not - he gives one to casino. If he …
      asked Jun 11 '13 by Alexander Chervov
      5
      votes
      3answers
      Consider any discrete time stochastic process $p(n)$ (price) with independent increments $\xi_k$ and $E(\xi_k)=0$. E.g. Brownian motion (i.e. $\xi_k = N(0,1)$). Consider some "trading strategy" whic …
      asked Jun 2 '13 by Alexander Chervov
      16
      votes
      3answers
      Background James-Stein estimator and Stein's phenomenon, as described in Wikipedia are rather counterintuitive and amazing. It is claimed that if one wants to estimate the mean $\Theta$ of Gaussian …
      asked Apr 11 '12 by Alexander Chervov
      1
      vote
      2answers
      Have the following stochastic process $f(t)$ been studied in mathematics ? It is stationary, Gaussian, $f(t)-$complex independent Gaussians $N(0,1)$. The autocorrelation is given by the zero-order Be …
      asked Mar 29 '12 by Alexander Chervov
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      Prices of financial assets (stock-market prices or currency exchange rates) obviously resemble trajectories of stochastic processes. What is known about their mathematical properties ? I know the …
      asked Apr 28 '13 by Alexander Chervov

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