Related papers: On the representation property for 1D general diff…
For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…
We prove that weakly continuous solutions to martingale problems admit a canonical regular conditional probability distribution. This allows for the construction of time consistent convex dynamic procedures in a non dominated setting.…
Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f, the backward Kolmogorov equation gives a condition for f(t,X) to be a local…
Semiconductor model is a system of parabolic partial differential equations with cross-diffusion phenomenon. Previous results showed that a weak solution exists and is not bounded in general. So semiconductor model was categorized as a…
We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra…
The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale.…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This…
We derive the explicit form of the martingale representation for square-integrable processes that are martingales with respect to the natural filtration of the super-Brownian motion. This is done by using a weak extension of the Dupire…
Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in…
We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of…
We consider a generic diffusion on the 1D torus and give a simple representation formula for the large deviation rate functional of its invariant probability measure, in the limit of vanishing noise. Previously, this rate functional had…
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…
Given a reference filtration $\mathbb{F}$, we develop in this work a generic method for computing the semimartingale decomposition of $\mathbb{F}$-martingales in some specific enlargements of $\mathbb{F}$. This method is then applied to the…
Given a general It\^o semimartingale, its Markovian projection is an It\^o process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for…
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
In this paper we obtain a martingale representation theorem in the progressive enlargement $\mathbb{G}$ by a random time $\tau$ of the filtration $\mathbb{F}^L$ generated by a L\'evy process $L$. The assumptions on the random time are that…
In this article, it is proved that for any cumulative distribution function with compact support and a specified t > 0, there exists a diffusion martingale which has this law at time t. The article proves existence; no claims are made about…