Related papers: $\natural$-model with jumps
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…
We study the convergence of $N-$particle systems described by SDEs driven by Brownian motion and Poisson random measure, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending…
This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master…
This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…
Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
We develop a notion of sampling, called \emph{generic sampling}, for the context of global Keisler measures where the standard product is replaced by the Morley product. Choosing a point randomly in this space with respect to our…
We propose a model for the credit markets in which the random default times of bonds are assumed to be given as functions of one or more independent "market factors". Market participants are assumed to have partial information about each of…
Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential…
Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the…
In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…
We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in post-selection as well as for real-time…
We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…