Hi, I'm sure x_t is a decreasing sequence while y_t is an increasing one. It feels like it should be simple to prove, but I just can't do it. Any suggestions would be great!(adsbygoogle = window.adsbygoogle || []).push({});

Thanks,

Peter

x_t and y_t are defined iteratively by two equations:

1. y_(t+1) = bq x_t + b(1 - q) y _t

2. f[x_(t+1)] = bqf[x_t] + b(1 - q) f[y _t]

IE

2B. x_(t+1) = f^(-1)[bqf[x_t] + b(1 - q) f[y _t]]

Other conditions:

1. f[x] is decreasing and concave

2. x_0 = 1

3. y_0 = 0

4. 0 < q < 1

5. 0 < b < 1

6. f(0) = 1

7. f(1) = 0

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# Proving sequence x_t is decreasing

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