Related papers: Some function spaces related to the Brownian motio…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
In this paper we investigate the Quantum Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless scalar field in (3 + 1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet, Neumann, mixed…
The Stretched Sierpinski Gasket is a non-self-similar set but it still exhibits very high symmetry. In an earlier work we calculated the leading term for the eigenvalue counting function for operators coming from resistance forms that were…
We extend the Poincar\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the…
A fractafold, a space that is locally modeled on a specified fractal, is the fractal equivalent of a manifold. For compact fractafolds based on the Sierpinski gasket, it was shown by the first author how to compute the discrete spectrum of…
In this paper, we study the existence and uniqueness of a class of stochastic differential equations driven by fractional Brownian motions with arbitrary Hurst parameter $H\in (0,1)$. In particular, the stochastic integrals appearing in the…
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This allows us to introduce…
We establish the procedure to derive from an action-based variational principle the classical equations of motion in Hamiltonian phase space of a particle subject to general position and velocity dependent non-holonomic equality…
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski…
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to…
We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a $(1,1)$-Poincar\'e inequality.…
We present a new approach to the theory of k-forms on self-similar fractals. We work out the details for two examples, the standard Sierpinski gasket and the 3-dimensional Sierpinski gasket, but the method is expected to be effective for…
Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the…
For a family of domains in the Sierpinski gasket, we study harmonic functions of finite energy, characterizing them in terms of their boundary values, and study their normal derivatives on the boundary. We characterize those domains for…
We study the existence of a unique solution to semilinear fractional backward doubly stochastic differential equation driven by a Brownian motion and a fractional Brownian motion with Hurst parameter less than 1/2. Here the stochastic…
We study the long-time behaviour of solutions to a class of $d$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)$. The drift consists of a dissipative Lipschitz term and a…
We study the relationship between the geometry of smoothly bounded domains in complete Riemannian manifolds and the associated sequence of $L^1$-norms of exit time moments for Brownian motion. We establish bounds for Dirichlet eigenvalues…
A new approach to the generalised Brownian motion introduced by M. Bozejko and R. Speicher is described, based on symmetry rather than deformation. The symmetrisation principle is provided by Joyal's notions of tensorial and combinatorial…
On the unit interval (I), and the Sierpinski Gasket ($\mathcal{SG}$), the spectral decimation function of the Laplacian has similar properties that result in positive minimum spacing of eigenvalues. Other fractals, for example the level-3…
We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue spaces. We prove…