Question
Leave X and Y alone free remarkable arbitrary factors with separate rates An and g. (a) Argue that: restrictive on X > Y, the irregular
Leave X and Y alone free remarkable arbitrary factors with separate rates An and g.
(a) Argue that: restrictive on X > Y, the irregular factors min(X, Y) and X-Yare autonomous.
(b) use section (a) to infer that for any certain steady c
Y)IX > Y +cl = Y)IX > Y]
1
(c) Give a verbal clarification ot why min(X, Y) and XYare (genuinely) free.
Q22
Let S(t) indicate the cost ota security at time t. A mainstream model for the cycle (S(t), t 2 0)
assumes that the value stays unaltered until a "stun" happens, at which time the cost is
increased by an irregular factor. Ifwe let N(t) mean the quantity of stuns by time t, and let Xi
indicate the multiplicative factor, at that point this model guesses that where
where Xi is equivalent to 1 when N(t) = 0. Assume that the are free remarkable
irregular factors with rate g; that {N(t), t 2 0} is a Poisson interaction witn rate A; that {N(t), t 2 0} is
free of the Xi and that S(O) = s.
(a) Find
(b) Find
Q23
Let 2 0), I l, be free Poisson measures with individual rates
l, 2 and set
+ M2(t) + M3(t)
The stochastic cycle ((NI(I), 20) is known as a bivariate Poisson measure.
(a) Find n, N2(t)
(b) Find N2(t))
Q24
Let 2 0), I l, be autonomous Poisson measures with particular rates
l, 2 and set
+ M2(t) + M3(t)
The stochastic cycle ((NI(I), 20) is known as a bivariate Poisson measure.
(a) Find n, N2(t)
(b) Find N2(t))
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