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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

1 vote
1 answer
291 views

Area under Gaussian sample path curve

Dear All, We know that the coastline paradox is related with fractal dimension of a curve. Now I want to know how to estimate the area under a sample path curve of a Gaussian process: Given a station …
honglangwang's user avatar
6 votes
2 answers
552 views

Inequality involving the weak second moment

I want to ask the following probability inequality: Is it true that for any random variable $X\ge 0$, we have $$ \sup_{t>0}(t\mathbb E(X\mathbf 1_{X\ge t})) \le 2\sup_{t>0}(t^2 \mathbb P(X \ge t …
honglangwang's user avatar
-2 votes
1 answer
248 views

for examples in probability [closed]

Give an example satisfying the following conditions: give out a sequence of random variables defined on a probability space, and a sub sigma algebra: the sequence converges almost surely to a limit an …
honglangwang's user avatar