Related papers: A Causal Construction of Diffusion Processes
We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling density, with the gradient of an arbitrary density of interest…
We consider the identification problem of a noncausal Ito process from its stochastic Fourier coefficients with respect to the complete system of trigonometric functions. Here, a noncausal Ito process is the extension of Ito process whose…
Generalizing Brownian motion (BM), fractional Brownian motion (FBM) is a paradigmatic selfsimilar model for anomalous diffusion. Specifically, varying its Hurst exponent, FBM spans: sub-diffusion, regular diffusion, and super-diffusion. As…
A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
For the concrete model of Brownian particles dynamics in non-uniform environment, the time interval estimation is constructed, on which phenomenological Fick laws for diffusion phenomenon description can be used. The knowledge of these…
In this paper, we demonstrate the simulation of fundamental solution for the parabolic equation by the relationship with Ito diffusion. The factorization and Monte Carlo methods of the fundamental solution are considered. With the fact that…
If X is a d-dimensional uniformly elliptic diffusion, with initial law nu, we show that F(X) is a Dirichlet process, whenever F satisfies an integrability condition linking its weak derivative to the coefficients of the diffusion and the…
We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related…
Within the framework of the previous paper [8]. we develop a generalized stochastic calculus for processes associated to higher order diffusion operators. Applications to the study of a Cauchy problem, a Feynman-Kac formula and a…
Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83--109] prove an extension of It\^{o}'s formula for $F(X_t,t)$, where $F(x,t)$ has a locally square-integrable derivative in $x$ that satisfies a mild continuity condition in $t$ and…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating…
By an extension of of some estimates due to Crandall and Pierre and Di Benedetto we derive consequences for fully nonlinear parabolic equations of the form $\dt v + F(t,x,D^2v)=0$, where $F$ can be both singular and degenerate elliptic and…
Motivated by recent development of mean-field systems with common noise, this paper establishes Ito's formula for flows of conditional probability measures under a common filtration associated with general semimartingales. This generalizes…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
This short note suggests special examples of stochastic Ito integrals with controlled growth of their containing range. The integrands for this integrals are presented explicitly. The construction does not involve neither stopping times nor…