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Results tagged with stochastic-processes
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user 17114
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
3
votes
Calculating the probability of an event defined by a condition on a Gaussian random process
I would recommend obtaining a copy of the text
H. Cramer and M. R. Leadbetter (1967), Stationary and Related Stochastic Processes, John Wiley & Sons, Inc.
which is available as a 2004 Dover repr …
- 1,136
7
votes
Accepted
Capped binomial random variables
The answer to your question is positive and, for example, follows immediately from Corollary 4 of
C. A. León and F. Perron (2003), Extremal properties of sums of Bernoulli random variables, Statis …
- 1,136
16
votes
Is the function $e^{x^2/2} \Phi(x)$ monotone increasing?
This is just an alternative argument to Davide's nice one.
First, note that $h' = e^{x^2/2}(x \Phi + \Phi')$.
Since $\Phi'' = -x \Phi'$, monotonicity of the integral yields
$$
x \Phi(x) \geq \int_{- …
- 1,136