Environmental Engineering Reference

In-Depth Information

Appendix C

List of symbols and acronyms

C.1 Greek symbols

α

average of the random heights of jumps in the compound

Poisson process

γ

growth factor

[

·

]

gamma function

δ

[

·

]

Dirac delta function

1
,

states of dichotomic noise

2

θ

threshold value

[

·

]

unit step function

κ

1dn
,

κ

first and second cumulants of dichotomous noise

2dn

κ

1gn
,

κ

first and second cumulants of Gaussian white noise

2gn

κ

κ

1sn
,

first and second cumulants of shot noise

2sn

λ

rate of the shot-noise process

ξ

noise term

ξ
cn

Gaussian colored-noise process

ξ
dn

dichotomous-noise process

ξ
gn

Gaussian-white-noise process

ξ
ou

Ornstein-Uhlenbeck process

ξ
per
(
t
)

periodical zero-mean forcing

ξ
sn

shot-noise process

ξ
sn

zero-average shot-noise process

ρ

(

·

)

drift term in the additive-shot-noise process

τ
1
,

τ
2

mean permanence time in a state of the dichotomic noise

τ
c

relaxation time

τ

correlation time of the Ornstein-Uhlenbeck process

ou

φ

state variable

φ

mode or antimode of the steady-state pdf of

φ

m

289

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