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Questions tagged [stochastic-processes]

For questions about stochastic processes, for example random walks and Brownian motion.

A stochastic process is a collection of random variables representing the evolution of a system of random variables over time. A typical example is a .

A stochastic, or random, process describes the correlation or evolution of random events. It is used to model stock market fluctuations and electronic/audio-visual/biological signals. Among the most well-known stochastic processes are random walks and Brownian motion.

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Introduction to Probability Models, Tenth Edition (Ross) Example 4.7 Questions

enter image description here enter image description here How was the state transition probability matrix obtained for this example question? I hope you can provide help, thank you!
ruifeng bai
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covariance function for Brownian motion

What is Cov[W(t),W(0)] when W(t) is t*B(1/t) and W(0) = 0 where B(t) is standard Brownian motion. The answer is min {s,t}. I am unsure how they get that because I get min{0,1}. Here is what I did: Cov[W(t),W(0)] = E[W(t)W(0)] = E[t*B(1/t)*B(0)] =…
icobes
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What is the expected value of the least time they are in the same edge?

There are 2 particles are positioned at the vertices of a cube. If at a given time $t$ the particles are in the same edge, then they remain in the same position up to time $t + 1$. Otherwise, one of them is chosen at random with equal probability,…
Jovoszhou
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Expected Duration of a Gambler's Ruin Game

I was reviewing over my notes and couldn't understand where the underline portion from attached note comes from and why it is a sum from k = 0 to x-1. This is with respect to a Gambler's ruin game with end points 0 and N and g(x) is our expected…
Mid
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Markov Chain is irreducible or not, and aperiodic or not.

states = {1,2,3,4} I'm confused if the following markov chain is irreducible or not. I think it's not irreducible because if it reaches from one state to another with probability 1 it stays there. I think it's not aperiodic as there are no self…
noname
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continuous-time stochastic process

Give an example of a continuous-time stochastic process (Xt)t≥0 which is not a martingale, but such that E[Xt] = 0 for all t ≥ 0. Hint: consider f(Wt), for a well-chosen function f (where (Wt)t≥0 is, as usual, a standard Brownian Motion).
Haroro Wong
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