In Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part I they define (on page 4) a metric :

$${\bf d}_\infty ((t,\omega),(t',\omega')) := |t-t'| + \|\omega_{.\wedge t}-{\omega'}_{.\wedge t'}\|_{T^.}$$

where :

$$\|\omega\|_t := \sup_{0\leq s \leq t}|\omega_s|$$

What do the dots in $.\wedge t$ and $T^.$ signify?

  • 5
    $\begingroup$ The first one that you take the whole path (which is then taken only up to t thanks to the minimum and stays from there on constant). The norm is a norm on the path space. The second one that this is the end of the sentence (period). $\endgroup$ Jun 24 '18 at 15:20
  • $\begingroup$ @StephanSturm Thanks. I had failed to notice that some of the other equations also had periods marking the end of the sentence:) $\endgroup$
    – deepblue
    Jun 24 '18 at 19:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.