相关论文: On the stochastic regularity of distorted Brownian…

For any starting point in $\mathbb{R}^d$, we identify the stochastic differential equation that is satisfied by distorted Brownian motion with respect to a certain discontinuous Muckenhoupt $A_2$-weight $\psi$. The discontinuities of $\psi$…

Using elliptic regularity results in weighted spaces, stochastic calculus and the theory of non-symmetric Dirichlet forms, we first show weak existence of non-symmetric distorted Brownian motion for any starting point in some domain $E$ of…

The aim of this paper is two-fold. On one hand, we will study the distorted Brownian motion on $\mathbb{R}$, i.e. the diffusion process $X$ associated with a regular and strongly local Dirichlet form obtained by the closure of…

In this work we connect the theory of Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is perturbed by a series of constant multiples of local times at a sequence of…

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…

The starting point is a gradient Dirichlet form with respect to $\varrho\lambda^d$ on the space $L^2({\mathbb{R}}^d, \varrho\mu)$. Here $\lambda^d$ is the Lebesgue measure on ${\mathbb R}^d$, $\varrho$ a strictly positive density and $\mu$…

We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,…

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be…

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a…

We study the long-time behaviour of solutions to a class of $d$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)$. The drift consists of a dissipative Lipschitz term and a…

We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…

Motivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we…

We consider the stochastic continuity equation perturbed by a fractional Brownian motion and the drift is allowed to be discontinuous. We show that for almost all paths of the fractional Brownian motion there exists a solution to the…

In this paper we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dW_{t}+b(t, X_{t})dt, \quad t\ge s, \quad X_{s}=x, \] where $b: [0,\infty) \times \mathbb{R}^{d} \to \mathbb{R}^{d}$ is a measurable…

We study a family of essentially pairwise independent Brownian motions indexed by a continuum of labels and show how the Fubini extension framework provides a rigorous way to represent such families as a single jointly measurable process.…

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann…