How many functions solve the Chapman-Kolmogorov equation? The Chapman-Kolmogorov equation is defined as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f({x_n}|{x_m}) = \int_{ - \infty }^{ + \infty } {f({x_n}|{x_o})} f({x_o}|{x_m})d{x_o}[/tex]

And I've seen it proved that the following function will satisfy the above condition:

[tex]f({x_n}|{x_o}) = {\left( {\frac{\lambda }{{2\pi ({t_n} - {t_0})}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$}

\kern-0.1em/\kern-0.15em

\lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{\frac{{\lambda {{({x_n} - {x_0})}^2}}}{{2({t_n} - {t_0})}}}}[/tex]

But I have to wonder if there are any other functions that satisfy it. Any help is appreciated.

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# Functions solving Chapman-Kolmogorov

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