Related papers: Characterization of max-continuous local martingal…
We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes…
We consider the local limit of finite uniformly distributed directed animals on the square lattice viewed from the root. Two constructions of the resulting uniform infinite directed animal are given: one as a heap of dominoes, constructed…
We consider local martingales which are standard or stochastic exponentials M of one component X of a multivariate affine process in the sense of Duffie, Filipovic and Schachermayer (2003). By completing their characterization of…
We examine the continuous-time counterpart of mirror descent, namely mirror flow, on classification problems which are linearly separable. Such problems are minimised `at infinity' and have many possible solutions; we study which solution…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
For a branching random walk that drifts to infinity, consider its Malthusian martingale, i.e.~the additive martingale with parameter $\theta$ being the smallest root of the characteristic equation. When particles are killed below the…
In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
We consider a supercritical branching process $Z_n$ in a stationary and ergodic random environment $\xi =(\xi_n)_{n\ge0}$. Due to the martingale convergence theorem, it is known that the normalized population size $W_n=Z_n/ (\mathbb E…
In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original…
The formalism of local maximization for entropy gradient producing the evolution and dynamical equations for closed systems. It eliminates the inconsistency between the reversibilty of time in dynamical equations and the strict direction of…
For one-dimensional diffusions on the half-line, we study a specific type of conditioning to avoid zero. We introduce supermartingales defined via concave functions with respect to the scale function. A conditioning is formulated through…
We consider measure-valued processes $X=(X_t)$ that solve the following martingale problem: for a given initial measure $X_0$, and for all smooth, compactly supported test functions $\varphi$, \begin{eqnarray*}X_t(\varphi…
We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…
Is this paper we study penalisations of diffusions satisfying some technical conditions, generalizing a result obtained by Najnudel, Roynette and Yor. If one of these diffusions has probability distribution $\mathbb{P}$, then our result can…
We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish…
We find a maximum principle for general non-Markovian semi-martingales. We do so by describing the adjoint processes with non-anticipating stochastic derivatives in a martingale random field setting. In the case of the L\'evy processes this…
A supermartingale deflator (resp., local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp., local martingales). The supermartingale numeraire (resp., local martingale numeraire) is…
In this paper we extend the stability results of [4]}. Our utility maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the…