Related papers: Integrability of solutions of the Skorokhod Embedd…
In this paper we introduce a numerical method for optimal stopping in the framework of one dimensional diffusion. We use the Skorokhod embedding in order to construct recombining tree approximations for diffusions with general coefficients.…
There are various situations in which it is natural to ask whether a given collection of $k$ functions, $\rho_j(\r_1,...,\r_j)$, $j=1,...,k$, defined on a set $X$, are the first $k$ correlation functions of a point process on $X$. Here we…
We derive a nonlinear integral equation to calculate Root's solution of the Skorokhod embedding problem for atom-free target measures. We then use this to efficiently generate bounded time-space increments of Brownian motion and give a…
We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful…
We consider several general conditions for integrability of two Roumieu ultradistributions and prove their equivalence. The discussed sequential conditions are based on two classes of approximate units and allow one to introduce sequential…
We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant because the boundary conditions can be…
SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. Integrated supOU…
In this note we consider autonomous SDEs admitting smooth invariant measures. We present a method in finding (almost everywhere) good bounds for $\sup \{\|X_t\|: t \in [0, T]\}$ for strong solutions $X_{\cdot}$ to such SDEs, which in many…
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward…
Expectation Propagation (EP) is a widely used iterative message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions as ``beliefs'' using intermediate functions called…
We consider the $3D$ spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We assume that the initial condition is a probability measure with finite energy and is not a Dirac mass. For hard potentials, we…
Simultaneous Embedding with Fixed Edges (SEFE) is a problem where given $k$ planar graphs we ask whether they can be simultaneously embedded so that the embedding of each graph is planar and common edges are drawn the same. Problems of SEFE…
We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is described by a step function, with a jump discontinuity across…
If a continuous map f: X->Q is approximable arbitrary closely by embeddings X->Q, can some embedding be taken onto f by a pseudo-isotopy? This question, called Isotopic Realization Problem, was raised by Shchepin and Akhmet'ev. We consider…
In this paper, we consider the 1D compressible Euler equation with the damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu <1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutions exist globally…
Recently, \cite{BeJu16, BeNuTo16} established that optimizers to the martingale optimal transport problem (MOT) are concentrated on $c$-monotone sets. In this article we characterize monotonicity preserving transformations revealing certain…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
Let $(X,\phi)$ be a compact flow without fixed points. We define the packing topological entropy $h_{\mathrm{top}}^P(\phi,K)$ on subsets of $X$ through considering all the possible reparametrizations of time. For fixed-point free flows, we…
We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form $\tfrac{\mu}{(1+t)^{\lambda}}$ in $\mathbb{R}^d$ $(d \geq 1)$. We establish uniform…
The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model…