Abstract nonlinear prediction and operator martingales

Martingales and the Beurling-ahlfors Operator, an Overview

Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

Continuous Martingales and Local Martingales

Throughout these notes, (Ω,F ,P ) will be a probability space and F := {Ft }t∈J a filtration indexed by J , where J is an interval, usually J = [0,∞). The filtration F is said to be complete if each Ft contains all sets of measure 0, and is right-continuous if Ft =∩s>t Fs . A standard filtration is a filtration that is both complete and right-continuous. A stochastic process {X t }t≥0 defined o...

Prediction Market Prices as Martingales: Theory and Analysis

Introduction With prediction markets growing in number and in prominence in various domains, the construction of a modeling framework for the behavior of prices on traded contracts has become an increasingly important endeavor. In this paper, we present such a theoretical framework, as we attempt to use mar-tingale theory in the analysis of prediction market price fluctuations. The application ...

Nonlinear Alternatives for Multivalued Maps with Applications to Operator Inclusions in Abstract Spaces

A nonlinear alternative of Leray–Schauder type is presented for condensing operators with closed graph. We will then use this theorem to establish new existence principles for differential and integral inclusions in Banach spaces.