Related papers: Strong Feller property via moment method
We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…
In this paper, we establish the strong well-posedness of SDEs with merely integrable time-dependent drifts driven by fractional Brownian motions with Hurst parameter H<1/2. Our result holds over the entire subcritical regime and can be…
This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes $(X(t),\Lambda(t))$, where $\Lambda(t)$ is a component representing discrete events taking values in a countably infinite…
Starting from the Caldeira-Leggett (CL) model, we derive the equation describing the Quantum Brownian motion, which has been originally proposed by Dekker purely from phenomenological basis containing extra anomalous diffusion terms.…
We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent…
Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead…
In this paper we study the moment generating function and the moments of occupation time functionals of one-dimensional diffusions. Assuming, specifically, that the process lives on $\mathbb{R}$ and starts at~0, we apply Kac's moment…
We prove that the any Markov solution to the 3D stochastic Navier-Stokes equations driven by a mildly degenerate noise (i.e.all but finitely many Fourier modes are forced) is uniquely ergodic. This follows by proving strong Feller…
We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain…
This thesis is dedicated to the study of stochastic processes; non-deterministic physical phenomena that can be well described by classical physics. The stochastic processes we are interested in are akin to Brownian Motion and can be…
We establish the existence and pathwise uniqueness of regime-switching diffusion processes in an infinite state space, which could be time-inhomogeneous and state-dependent. Then the strong Feller properties of these processes are…
We give a new example of a measure-valued process without a density, which arises from a stochastic partial differential equation with a multiplicative noise term. This process has some unusual properties. We work with the heat equation…
In this paper, we establish the existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by Brownian motion on a bounded domain $D$ in the setting of $L^2(D)$ space. The result is valid for all…
This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…
We address the long time behavior of solutions of the stochastic Korteweg-de Vries equation $ du + (\partial^3_x u +u\partial_x u +\lambda u)dt = f dt+\Phi dW_t$ on ${\mathbb R}$ where $f$ is a deterministic force. We prove that the Feller…
We investigate the sensing performance of a single-qubit quantum thermometer within a non-Markovian dynamical framework. By employing an exactly numerical hierarchical equations of the motion method, we go beyond traditional paradigms of…
In [4], it is proved that we can have a continuous first-passage-time density function of one dimensional standard Brownian motion when the boundary is H\"older continuous with exponent greater than 1/2. For the purpose of extending [4]…
The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the…