## New answers tagged oc.optimization-and-control

1
vote

### (Sub)Optimality of random transport

The reference for the fact that $r$ gets matched to $F_B^{-1}(F_R(r))$ can be found in Theorem 2.9 of [1]. In one-dimensional optimal transport, this is known as the monotone map. I believe that the ...

5
votes

Accepted

### Which coupling minimises the following cyclic sum?

The sum in the excpected value is bounded below by $n$ (by the arithmetic-geometric mean inequality). The lower bound is achieved when all the variables are equal. Whence the value of you minimum is $...

5
votes

### What do smooth signatures give you?

The signature of a bounded variation path characterizes this path up to tree like equivalence
B. Hambly, T. Lyons: Uniqueness for the signature of a path of bounded variation and the reduced path ...

3
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### Elliptic PDEs in BSDEs and in optimal control

I’ll see if I have time to write a proper answer later, but if you consider stochastic games a form of control problem, then tug of war games are intimately connected to the $p$-Laplacian, which is an ...

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