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

**3**

votes

**2**answers

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

**1**answer

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

**3**answers

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

**3**answers

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

**2**answers

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

**0**

votes

**1**answer

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