Related papers: A pathwise inference method for the parameters of …
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the…
In this paper, we consider the robust adaptive non parametric estimation problem for the drift coefficient in diffusion processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed.…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
This paper proves a Krylov-Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and uniqueness of invariant probability measures for the process…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
Inspired by allocation strategies in multi-armed bandit model, we propose a pathwise construction of Walsh spider diffusions. For any infinitesimal generator on a star shaped graph, there exists a unique time change associated with a…
The global-in-time existence of bounded weak solutions to the Maxwell-Stefan-Fourier equations in Fick-Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and and the energy balance…
Much effort has been put into developing theories for dense fluids, as a result of these efforts many theories work for a certain type of particle or in a certain concentration regime. Rosenfeld proposed a dependence of the self-diffusion…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ans\"atze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some…
In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of…
A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…
This paper derives the exact transition density and cumulative distribution function of a linear combination of two independent Cox-Ingersoll-Ross (CIR) processes. By combining the Poisson Gamma mixture representation of the noncentral…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on the eigenfunctions of the diffusion operator. Since a Bessel process is non-ergodic and the theory of martingale…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…