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If a continuous-time process $x_t$ is geometric brownian motion it would have this property, or the discrete-time equivalent (geometric random walk).

A difference in logs is is (for $u_t$ small at least) effectively a percentage change.

See also the connection to the force of mortality (what actuaries used to call the hazard function, they seem to be using it less these days) and the force of interest, which are 'instantaneous' equivalents of your annualized (or more generally, periodized) discrete measure.

If a continuous-time process $x_t$ is geometric brownian motion it would have this property, or the discrete-time equivalent (geometric random walk).

A difference in logs is is (for $u_t$ small at least) effectively a percentage change.

See also the connection to the force of mortality (what actuaries used to call the hazard function, or rather they seem to be using it less these days) and the force of interest, which are 'instantaneous' equivalents of your annualized (or more generally, periodized) discrete measure.

If a continuous-time process $x_t$ is geometric brownian motion it would have this property, or the discrete-time equivalent (geometric random walk).

A difference in logs is is (for $u_t$ small at least) effectively a percentage change.

See also the connection to the force of mortality (what actuaries used to call the hazard function) and the force of interest, which are 'instantaneous' equivalents of your annualized (or more generally, periodized) discrete measure.

If a continuous-time process $x_t$ is geometric brownian motion it would have this property, or the discrete-time equivalent (geometric random walk).

A difference in logs is is (for $u_t$ small at least) effectively a percentage change.

See also the connection to the force of mortality (what actuaries used to call the hazard function, they seem to be using it less these days) and the force of interest, which are 'instantaneous' equivalents of your annualized (or more generally, periodized) discrete measure.

If a continuous-time process $x_t$ is geometric brownian motion it would have this property, or the discrete-time equivalent (geometric random walk).

If a continuous-time process $x_t$ is geometric brownian motion it would have this property, or the discrete-time equivalent (geometric random walk).

A difference in logs is is (for $u_t$ small at least) effectively a percentage change.

See also the connection to the force of mortality (what actuaries used to call the hazard function) and the force of interest, which are 'instantaneous' equivalents of your annualized (or more generally, periodized) discrete measure.