il. | re tx;-1)dx; =1 
iii. pi(%j,%) = [ press tedpatsnt— tabs. 
Generally, the Markov process is defined as follows, using the conditional 
probability when the probability, that X(t) is in the range x; — x;+ dx; at 4, under 
the condition that 
X(t) is oF] Ps +dx;1, at 1, 
xj-2 X;-2 + dx;_2, at tj2, 
X2 — 12+ dx, at tp, 
Xx; — X,+ dx, at ty, 
is determined by the conditional probability that X(r) is x; — x; + dx;, under the condi- 
tion that at only one preceding time step f = tj, x(t) 18 x-1, then this process is 
called a Markov process. Namely, if 
JOC EPSP IGCPOLIROR oo 5 8 BADUBES HH) 
SY CREPE) (12.4) 
this process X(t) is a Markov process. 
From Eg. 12.3 and Eq. 12.4, generally 
DACE pEPIE ETS 6 a 6 LPHUBES UN) Je Cry be sil) 
oS JO MCP IRCE ORE SP 6 0 6 AM PRAM UL (12.5) 
Therefore, by the same relation, 
Pr(&n, tn Xn-1,ln-1; > - - X2, 123X1, ty) 
= Do (Xn, Clete tn-1) Pe{Xn-1, tell; tn-2) sos 
X Pe,(X2, talx1, t1)p1@1, ¢1). (12.6) 
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