Related papers: Stochastic Integrals and Abelian Processes
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular cases the solutions of such an equations are the well-known…
Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…
We introduce an elementary method for proving the absolute continuity of the time marginals of one-dimensional processes. It is based on a comparison between the Fourier transform of such time marginals with those of the one-step Euler…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…
We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site. The construction only requires the…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
In this paper, we consider the problem of steering a family of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by using an…
In this note, we discuss the uniform ergodicity of a diffusion process given by an It\^o stochastic differential equation. We present an integral condition in terms of the drift and diffusion coefficients that ensures the uniform ergodicity…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
Sampling experiments provide a viable route to show quantum advantages of quantum devices over classical computers in well-defined computational tasks. However, quantum devices such as boson samplers are susceptible to various errors,…
In this paper a quantum mechanical phase space picture is constructed for coarse-grained free quantum fields in an inflationary Universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase…
This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous.…
The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form…