Related papers: Total variation distance between a jump-equation a…
We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or…
We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…
We uncover a universal scaling law governing the dispersion of collective attention and identify its underlying stochastic criticality. By analysing large-scale ensembles of Wikipedia page views, we find that the variance of logarithmic…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
The main result of this article establishes strong convergence rates on the whole probability space for explicit space-time discrete numerical approximations for a class of stochastic evolution equations with possibly non-globally monotone…
We consider the time discretization of fractional stochastic wave equation with Gaussian noise, which is negatively correlated. Major obstacles to design and analyze time discretization of stochastic wave equation come from the…
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…
Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment…
We establish an integration by parts formula for the semi-group in time $T > 0$ of the kinetic Brownian motion in the Euclidean plane together with its speed in the circle. The stochastic differential equation of our kinetic Brownian motion…
We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the H\"older constant of the Hessian of…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on $\mathbb{Z}^d$ with $d\geq1$, and gives a…
Consider the following stochastic differential equation for $(X_t)_{t\ge 0}$ on $\mathbb R^d$ and its Euler-Maruyama (EM) approximation $(Y_{t_n})_{n\in \mathbb Z^+}$: \begin{align*} &d X_t=b( X_t) d t+\sigma(X_t) d B_t, \\ &…
We consider the following second-order stochastic differential equation on $\mathbb{R}^{2d}$: \begin{equation*} dX_t^m=Y_t^mdt, \quad mdY_t^m=b(X_t^m)dt+\sigma(X_t^m)dB_t-Y^m_tdt, \end{equation*} where $X^m_t$ and $Y^m_t$ represent the…
Continuous-time random walks (CTRWs) with drift and position-dependent jumps provide a general framework for describing a wide range of natural and engineered systems. We analyze the stochastic differential equation associated with this…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
In this paper, we study a class of stochastic optimal control problem with jumps under partial information. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic…