Package jline.api.mc

Class Smp_passage_moments

java.lang.Object

jline.api.mc.Smp_passage_moments

public final class Smp_passage_moments
extends Object

Moments of order 1..nmax of the first passage time into a target state set for a SEMI-MARKOV chain with embedded transition matrix P.

Reference: P. G. Harrison and W. J. Knottenbelt, "Passage Time Distributions in Large Markov Chains", 2002, Sec. 3.2. This class implements Eq. 7 with the u_i(r) recurrence of Eq. 8,

     u_i(r) = -sum_{j=1..r} C(r,j) m_i(j) u_i(r-j),   u_i(0) = 1,
 

which are the derivatives at the origin of 1/h*_i(s). It is the branch for a holding time that depends only on the CURRENT state, and is cheaper than the full Eq. 6 kernel because it needs no per-pair moments.

Unlike the Markov case the n-th moment needs every moment from 1 to n, so nmax cannot be raised for free.

See Also:

• the Markov case, which this reproduces exactly when the holding times are exponential

Method Summary

Modifier and Type	Method	Description
static PassageMomentsResult	smp_passage_moments(Matrix P, Matrix hmom, Matrix pi0, int[] target, int nmax)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

smp_passage_moments

public static PassageMomentsResult smp_passage_moments(Matrix P,
 Matrix hmom,
 Matrix pi0,
 int[] target,
 int nmax)

Parameters:

P - embedded transition matrix, rows summing to one

hmom - (nstates x nmax): hmom(i,r-1) is the r-th moment of the sojourn in state i

pi0 - initial distribution, or null for per-state results only

target - 0-based target state indices