Related papers: Large deviations of the stochastic area for linear…

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

In the recent article [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily slow convergence speed and every natural number $d \in…

We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary…

We consider non degenerate Brownian SDEs with H{\"o}lder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to…

We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous…

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…

We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew…

In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…

The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < \beta < \alpha \le 2$, where $0 < \beta \le 1$ and $0 < \alpha \le 2$ are the fractional…

Constructions of numerous approximate sampling algorithms are based on the well-known fact that certain Gibbs measures are stationary distributions of ergodic stochastic differential equations (SDEs) driven by the Brownian motion. However,…

The Airy$_{\beta }$ random point fields ($ \beta = 1,2,4$) are random point fields emerging as the soft-edge scaling limits of eigenvalues of Gaussian random matrices. We construct the unlabeled diffusion reversible with respect to the…

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

We study a voting model on a branching Brownian motion process on $\mathbb{R}$ in which the diffusivity of each child particle is increased from that of the parent by a factor of $\gamma>1$. The probability distribution of the overall vote…

This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDDSEs) in a convex domain D. Moreover, using a stochastic flow approach a probabilistic interpretation for a…

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a mean flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding…

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…

We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…

Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…