相关论文: Approximations of a complex Brownian motion with p…

Gonzalez Cazares and Ivanovs (2021) suggested a new method for "recovering" the Brownian motion component from the trajectory of a Levy process that required sampling from an independent Brownian motion process. We show that such a…

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends…

We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…

We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional $\alpha$-stable processes, and multistable processes,…

We give asymptotic estimations on the area of the sets of points with large Brownian winding, and study the average winding between a planar Brownian motion and a Poisson point process of large intensity on the plane. This allows us to give…

This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the…

We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external…

We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise…

We consider the median of n independent Brownian motions, and show that this process, when properly scaled, converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct…

We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…

It is shown that many of the classical generalized isoperimetric inequalities for the Laplacian when viewed in terms of Brownian motion extend to a wide class of Levy processes. The results are derived from the multiple integral…

We consider the maximum process of a random walk with additive independent noise in form of $\max_{i=1,\dots,n}(S_i+Y_i)$. The random walk may have dependent increments, but its sample path is assumed to converge weakly to a fractional…

A variational representation for functionals of G-Brownian motion is established by a finite-dimensional approximate technique. As an application of the variational representation, we obtain a large deviation principle for stochastic flows…

We define a time dependent empirical process based on $n$ independent fractional Brownian motions and describe strong approximations to it by Gaussian processes. They lead to strong approximations and functional laws of the iterated…

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 construct a stochastic process, called the Liouville Brownian motion, which is the Brownian motion associated to the metric $e^{\gamma X(z)}\,dz^2$, $\gamma<\gamma_c=2$ and $X$ is a Gaussian Free Field. Such a process is conjectured to…

Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…

We investigate a random integral which provides a natural example of an imaginary exponential functional of Brownian motion. This functional shows up in the study of the binary annihilation process, within the Doi-Peliti formalism for…

Conditional independence and graphical models are crucial concepts for sparsity and statistical modeling in higher dimensions. For L\'evy processes, a widely applied class of stochastic processes, these notions have not been studied. By the…

We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…