相关论文: Making Birth-Death Processes from Backward Fokker-…

We propose a novel stochastic method to generate paths conditioned to start in an initial state and end in a given final state during a certain time $t_{f}$. These paths are weighted with a probability given by the overdamped Langevin…

For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time…

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…

Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…

This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…

When computing the expected value of time till extinction of a Birth and Death process, the usual textbook approach results in an extreme case of numerical ill-conditioning, which prevents us from getting accurate answers beyond the first…

As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master…

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…

The limitations resulting from the dichtomisation of continuous outcomes have been extensively described. But the need to present results based on binary outcomes in particular in health science remains. Alternatives based on the…

Expectations of path integrals of killed stochastic processes play a central role in several applications across physics, chemistry, and finance. Simulation-based evaluation of these functionals is often biased and numerically expensive due…

We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…

In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and…

We provide forecasts for mortality rates by using two different approaches. First we employ dynamic non-linear logistic models based on Heligman-Pollard formula. Second, we assume that the dynamics of the mortality rates can be modelled…

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…

The estimation of equations from data is of interest in physics. One of the famous methods is the sparse identification of nonlinear dynamics (SINDy), which utilizes sparse estimation techniques to estimate equations from data. Recently, a…

Many stochastic differential equations in various applications like coupled neuronal oscillators are driven by time-periodic forces. In this paper, we extend several data-driven computational tools from autonomous Fokker-Planck equation to…

This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…