Related papers: Convexity preserving jump-diffusion models for opt…

This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…

We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…

Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…

Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has sought to characterize, detect, and mitigate memorization, the fundamental…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally…

This article is concerned with a mutualism ecological model with Levy noise. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied.…

We consider the so-called $\natural$-model. It is an one-default model which gives the conditional law of a random time with respect to a reference filtration. This model has been studied in the case where the parameters are continuous. In…

Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…

In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…

This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are…

Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem…

Conditional diffusion probabilistic models can model the distribution of natural images and can generate diverse and realistic samples based on given conditions. However, oftentimes their results can be unrealistic with observable color…

Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…

Driven-dissipative protocols are proposed to control and create nontrivial quantum many-body correlated states. Protocols conserving the number of particles stand apart. As well-known, in quantum systems with the unitary dynamics the…

Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…

In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions to SDE's. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate Markov property. To…

Diffusion generative models have demonstrated remarkable success in visual domains such as image and video generation. They have also recently emerged as a promising approach in robotics, especially in robot manipulations. Diffusion models…