An Introduction to Stochastic Processes: With Special Reference to Methods and Applications |
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Page 11
... example , if events are occurring independently and randomly in time , a specification of the random function N ( t ) , representing the total number of events at time t , could be given in terms of the random times T1 , T2 , ... at ...
... example , if events are occurring independently and randomly in time , a specification of the random function N ( t ) , representing the total number of events at time t , could be given in terms of the random times T1 , T2 , ... at ...
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... example ) . Example 2. As a less trivial example , suppose f ( x ) = fxe - t g ( x , λ ) = ( μ / √λ ) e - μ≈ sinh ( μx √λ ) ( x≤t ) . Then we find P ( Y ) = ( [ 1 + ¥ / μ ] 2 - λ ) -1 , whence To obtain P ( A ) we may use formula ...
... example ) . Example 2. As a less trivial example , suppose f ( x ) = fxe - t g ( x , λ ) = ( μ / √λ ) e - μ≈ sinh ( μx √λ ) ( x≤t ) . Then we find P ( Y ) = ( [ 1 + ¥ / μ ] 2 - λ ) -1 , whence To obtain P ( A ) we may use formula ...
Page 176
... example , if we take giving f ( w ) = ! 2 1 πμε + ω στ a ( w ) = √ ( 2π ) ( μ + iw ) ' ẞ ( u ) = σe - μu ( u > 0 ) . More generally when f ( w ) is of the form n C2 ÏÏ ( w — w ̧ ) ( w — w ‡ ) 8 = 1 m - II ( w - wg ) ( w - w * ) s = n + ...
... example , if we take giving f ( w ) = ! 2 1 πμε + ω στ a ( w ) = √ ( 2π ) ( μ + iw ) ' ẞ ( u ) = σe - μu ( u > 0 ) . More generally when f ( w ) is of the form n C2 ÏÏ ( w — w ̧ ) ( w — w ‡ ) 8 = 1 m - II ( w - wg ) ( w - w * ) s = n + ...
Contents
RANDOM SEQUENCES | 15 |
PROCESSES IN CONTINUOUS TIME | 45 |
MISCELLANEOUS STATISTICAL APPLICATIONS | 89 |
Copyright | |
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a₁ additive process analysis approximate assumed asymptotic autoregressive average BARTLETT becomes Chapter characteristic function coefficients component condition consider continuous convenient convergence correlation correlogram corresponding covariance D. G. Kendall defined degrees of freedom denotes density depend differential discrete distribution function dZ(w entropy equation equivalent estimates example finite formula frequency further given harmonic harmonic analysis Hence independent individual infection integral interval J. R. Statist Kendall likelihood function limiting linear process Markov chain Markov process matrix mean methods Moyal mutation negative binomial distribution noise non-zero normal observed obtain orthogonal particle particular periodogram Poisson distribution population possible probability problem process X(t properties random variable recurrence relation renewal result sampling sequence solution spectral spectrum stationary processes stochastic processes t₁ theoretical theory time-series tion transition values variance vector whence zero σ²