Related papers: Filtration shrinkage by level-crossings of a diffu…
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion.…
Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $\text{d}\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two…
In this paper, we investigate a stochastic approximation procedure $\left(X_n\right)_{n\ge 0}$ taking values in $R$. The process is adapted to a filtration $(F_n)_{n\ge 0}$ and satisfies the recursion…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
We deal with various alternative decompositions of F-martingales with respect to the filtration G which represents the enlargement of a filtration F by a progressive flow of observations of a random time that either belongs to the class of…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The…
Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection and the so-called submartingale problem. We introduce a general formulation of the submartingale problem for…
In this article, it is proved that for any cumulative distribution function with compact support and a specified t > 0, there exists a diffusion martingale which has this law at time t. The article proves existence; no claims are made about…
The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…
Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…
We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the…
The paper analyses the sensitivity of the finite time horizon boundary non-crossing probability $F(g)$ of a general time-inhomogeneous diffusion process to perturbations of the boundary $g$. We prove that, for boundaries $g\in C^2,$ this…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…
We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it…
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…