Infinitesimal Calculus of Random Walk and Poisson Processes
Infinitesimal Calculus of Random Walk and Poisson Processes
Infinitesimal Calculus of Random Walk and Poisson Processes
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Gauge Institute Journal,<br />
H. Vic Dannon<br />
2 2<br />
0<br />
+ −<br />
0<br />
≤<br />
0<br />
+ −<br />
0<br />
{ EX [ ( ζ, t dt) X( ζ, t )]} E{[ X( ζ, t dt) X( ζ, t )] }<br />
<br />
Hence,<br />
≥0 ifinitesimal<br />
{ EX [ ( ζ, t + dt) − X( ζ, t )]} = infinitesimal,<br />
0 0<br />
EX [ ( ζ, t + dt) − X( ζ, t )] = infinitesimal.<br />
0 0<br />
2<br />
34