Free monotone transport

Monotone Martingale Transport Plans and Skorohod Embedding

We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod embedding which allows us to give a short proof of uniqueness.

Linear Transport Equations with mu-Monotone Coefficients

Matching Free Trees, Maximal Cliques, and Monotone Game Dynamics

Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal common subtrees. We then solve the problem using simple payoff-monotonic dynamics from evolutionary game theory. We illustrate the power of the...

On k-Monotone Approximation by Free Knot Splines

Let SN,r be the (nonlinear) space of free knot splines of degree r − 1 with at most N pieces in [a, b], and let M be the class of all k-monotone functions on (a, b), i.e., those functions f for which the kth divided difference [x0, . . . , xk]f is nonnegative for all choices of (k+1) distinct points x0, . . . , xk in (a, b). In this paper, we solve the problem of shape preserving approximation ...

On monotone and convex approximation by splines with free knots

We prove that the degree of shape preserving free knot spline approximation in L p a; b], 0 < p 1 is essentially the same as that of the non-constrained case. This is in sharp contrast to the well known phenomenon we have in shape preserving approximation by splines with equidistant knots and by polynomials. The results obtained are valid both for piecewise polynomials and for smooth splines wi...