Exp OU Process
Exp OU Process is a direct subtype of Stoch Process
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE Exp OU Process
This type represents an exponential Ornstein Uhlenbeck stochastic process with jumps.
It is driven by 3 independent stochastic factors, x, J and N, representing respectively the continuous diffusion part, the random jump size and random timing of each jump.
Formally the diffusion equation of the stochastic process s is:
s = eˣ⁺ʸ
where x is an Ornstein Uhlenbeck process dx = θ(μ-x)dt + σdw as described in Extended OU Process and y is a jump diffusion following the equation:
dy(t) = -βy(t-)dt + J(t)dN(t)
where β is constant, y(t-) is the prior to jump value of y at time t, J(t) is an independent identically distributed (iid) process representing the jump size and N is a Poisson-process with intensity λ
More specifically, at each t, J(t) is exponentially distributed with rate η, with the probability density function ηe⁻ᶯᴶ
Those 1/η is interpreted as the mean jump size in the evolution of y.
Web references available here and here