Related papers: Bismut Formulae and Applications for Functional SP…

We close an unexpected gap in the literature of stochastic differential equations (SDEs) with drifts of super linear growth (and random coefficients), namely, we prove Malliavin and Parametric Differentiability of such SDEs. The former is…

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…

Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…

A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…

A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and…

By using the local dimension-free Harnack inequality established on incomplete Riemannian manifolds, integrability conditions on the coefficients are presented for SDEs to imply the non-explosion of solutions as well as the existence,…

Hermite basis functions are a powerful tool for the spatial discretisation of Schr\"odinger equations with harmonic potential. In this work, we show that their stability properties extend to the simulation of Schr\"odinger equations without…

Stochastic partial differential equations (SPDEs) are often difficult to solve numerically due to their low regularity and high dimensionality. These challenges limit the practical use of computer-aided studies and pose significant barriers…

In this work, we will show the existence and uniqueness of the solution to the semi linear stochastic differential equations driven by weighted fractional Brownian motion with delay. We also prove smoothness of the density of the solution…

In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…

The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a…

This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker…

The existence and uniqueness of the mild solutions for a class of degenerate functional SPDEs are obtained, where the drift is assumed to be H\"{o}lder-Dini continuous. Moreover, the non-explosion of the solution is proved under some…

We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients…

In this paper we consider a class of stochastic differential equations driven by subordinate Brownian motion with Markovian switching. We use Malliavin calculus to study the smoothness of the density for the solution under uniform…

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…

Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system's dynamics. It applies to…

In the paper, Harnack inequalities are established for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H<1/2$. As applications, strong Feller property, log-Harnack inequality and entropy-cost…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…