Related papers: Comparison Theorem for Functional SDEs Driven by $…
In this paper, we study direct and inverse images for fractional stochastic tangent sets and we establish the deterministic necessary and sufficient conditions that guarantee that the solution of a given stochastic differential equation…
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…
In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via…
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent SDEs containing running…
Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…
By the methods of probability and duality technique, we give some comparison theorems for the solutions of infinite horizon forward-backwad stochastic differential equations.
Causal inference is a crucial goal of science, enabling researchers to arrive at meaningful conclusions regarding the predictions of hypothetical interventions using observational data. Path models, Structural Equation Models (SEMs), and,…
Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their own signature, i.e. of iterated integrals of the process…
The conformal invariance of Brownian motion is used to give a short proof of the Open Mapping Theorem for analytic functions.
We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H > 1/2 have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on…
We consider a system of stochastic differential equations driven by a standard n-dimensional Brownian motion where the drift coefficient satisfies a Novikov-type condition while the diffusion coefficient is the identity matrix. We define a…
In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators, the $z$ parts of whose $l$-th components only depend on the…
We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-R\"ockner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion.…
Let $X$ be a regular one-dimensional transient diffusion and $L^y$ be its local time at $y$. The stochastic differential equation (SDE) whose solution corresponds to the process $X$ conditioned on $[L^y_{\infty}=a]$ for a given $a\geq 0$ is…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…
Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.
The problem of model selection in the context of a system of stochastic differential equations (SDEs) has not been touched upon in the literature. Indeed, properties of Bayes factors have not been studied even in single SDE based model…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
In terms of a nice reference probability measure, integrability conditions on the path-dependent drift are presented for (infinite-dimensional) degenerate PDEs to have regular positive solutions. To this end, the corresponding stochastic…
We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…