Related papers: Perpetual integral functionals of diffusions and t…

We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability... The usual procedure is to use discretiza-tion schemes…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

For real-valued additive process $(X\_t)\_{t\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $$I\_{s,t}= \int \_s^t\exp(-X\_u)du, \quad 0\leq s<t\leq\infty, $$ in case the Laplace exponent of $X\_t$…

We investigate the feasibility of modelling turbulence via numeric functional integration. By transforming the Burgers' equation into a functional integral we are able to calculate equal-time spatial correlation of system variables using…

A fractional diffusion equation based on Riemann-Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of $H$-functions. It differs from the known…

We study boundary traces of shift-invariant diffusions: two-dimensional diffusions in the upper half-plane $\mathbb{R} \times [0, \infty)$ (or in $\mathbb{R} \times [0, R)$) invariant under horizontal translations. We prove that the…

We address the problem of minimizing the expected first-passage time of a Brownian motion with Poissonian resetting, with respect to the resetting rate $r.$ We consider both the one-boundary and the two-boundary cases.We investigate the…

The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…

The initial inverse problem of finding solutions and their initial values ($t = 0$) appearing in a general class of fractional reaction-diffusion equations from the knowledge of solutions at the final time ($t = T$). Our work focuses on the…

We study a one-dimensional diffusion process in a drifted Brownian potential. We characterize the upper functions of its hitting times in the sense of Paul L\'evy, and determine the lower limits in terms of an iterated logarithm law.

For birth-and-death processes, we show that every initial distribution is reproduced from the first hitting time distribution. The reproduction is done by applying to the distribution function a differential operator defined through the…

Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…

A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…

Adapting pretrained image-based diffusion models to generate temporally consistent videos has become an impactful generative modeling research direction. Training-free noise-space manipulation has proven to be an effective technique, where…

We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the particular case of transient Bessel processes,…