Related papers: Conditioning diffusion processes with killing rate…
We discuss equivalent formulations of the control of conditional processes introduced by Lions. In this problem, a controlled diffusion process is killed once it hits the boundary of a given domain and the controller's reward is computed…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However,…
We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…
Let $\mathcal{K}\subset R^d$, $d\ge2$, be a smooth, bounded domain satisfying $0\in\mathcal{K}$, and let $f(t),\ t\ge0$, be a smooth, continuous, nondecreasing function satisfying $f(0)>1$. Define $D_t=f(t)\mathcal{K}\subset R^d$. Consider…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
Recent progress with conditional image diffusion models has been stunning, and this holds true whether we are speaking about models conditioned on a text description, a scene layout, or a sketch. Unconditional image diffusion models are…
Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…
We study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We focus on sparse initial conditions where…
Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory…
This article gives conditions on a probability measure and drift field b such that for a given killing field k and a given time t > 0, there is function a such that there is a time homogeneous Markov process with infinitesimal generator…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
In this paper, the conditional phase distribution of the two-wave with diffuse power (TWDP) process is derived as a closed-form and as an infinite-series expression. For the obtained infinite series expression, a truncation analysis is…
Score-based diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which…
Diffusion processes are fundamental in modelling stochastic dynamics in natural sciences. Recently, simulating such processes on complicated geometries has found applications for example in biology, where toroidal data arises naturally when…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…