Related papers: Martingale representations in progressive enlargem…

Let $\mathfrak{z}$ be a stochastic exponential, i.e., $\mathfrak{z}_t=1+\int_0^t\mathfrak{z}_{s-}dM_s$, of a local martingale $M$ with jumps $\triangle M_t>-1$. Then $\mathfrak{z}$ is a nonnegative local martingale with $\E\mathfrak{z}_t\le…

Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…

We develop the mathematics of a filtration shrinkage model that has recently been considered in the credit risk modeling literature. Given a finite collection of points $x_1<...<x_N$ in $\mathbb{R}$, the region indicator function $R(x)$…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.

We prove the max-martingale conjecture given in recent article with Marc Yor. We show that for a continuous local martingale $(N\_t:t\ge 0)$ and a function $H:R x R\_+\to R$, $H(N\_t,\sup\_{s\leq t}N\_s)$ is a local martingale if and only…

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…

Let $r \leqslant n$ be nonnegative integers, and let $N = \binom{n}{r} - 1$. For a matroid $M$ of rank $r$ on the finite set $E = [n]$ and a partial field $k$ in the sense of Semple--Whittle, it is known that the following are equivalent:…

In this paper, we study existence and uniqueness of strong as well as weak solutions for general time fractional Poisson equations. We show that there is an integral representation of the solutions of time fractional Poisson equations with…

The classical Donsker weak invariance principle is extended to a Besov spaces framework. Polygonal line processes build from partial sums of stationary martingale differences as well independent and identically distributed random variables…

Minimally entangled typical thermal states (METTS) are a construction that allows one to to solve for the imaginary time evolution of quantum many body systems. By using wave functions that are weakly entangled, one can take advantage of…

The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…

We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…

We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of for00504925mulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in…

We consider a general piecewise deterministic Markov process (PDMP) $X=\{X_t\}_{t\geqslant 0}$ with measure-valued generator $\mathcal{A}$, for which the conditional distribution function of the inter-occurrence time is not necessarily…

This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a…

We show that a continuous local martingale is a strict local martingale if its supremum process is not in $ L_\alpha$ for a positive number $\alpha $ smaller than $1$. Using this we construct a family of strict local martingales.

In this paper we discuss existence and uniqueness for a one-dimensional time inhomogeneous stochastic differential equation directed by an $\mathbb{F}$-semimartingale $M$ and a finite cubic variation process $\xi$ which has the structure…

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The…