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SOLUTIONS
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Parametric Random Processes
Parametric random processes are processes specified using a few parameters. They provide standard models for a variety of areas, including finance (interest rates, ...), insurance (claims process, ...), and physics (radioactive decay, ...).
Mathematica provides complete support for working with parametric random processes. The symbolic representation of a process makes it easy to simulate its behavior, estimate parameters from data, and compute state probabilities at different times. There is a full suite of standard properties, including state distributions at different times as well as mean and covariance functions.
ReferenceReference
Discrete Time and Discrete State
RandomWalkProcess — random walk on infinite lattice
BernoulliProcess ▪ BinomialProcess ▪ RenewalProcess ▪ CompoundRenewalProcess
Discrete Time and Continuous State
Continuous Time and Discrete State
PoissonProcess — Poisson counting process
TelegraphProcess ▪ CompoundPoissonProcess ▪ RenewalProcess ▪ CompoundRenewalProcess
Continuous Time and Continuous State
WienerProcess — integrated Gaussian white noise
OrnsteinUhlenbeckProcess ▪ BrownianBridgeProcess ▪ GeometricBrownianMotionProcess ▪ CoxIngersollRossProcess ▪ FractionalBrownianMotionProcess ▪ CompoundPoissonProcess ▪ CompoundRenewalProcess
