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Model approximations are common practice when estimating structural or quasi-structural models. The paper considers the econometric properties of estimators that utilize projections to reimpose information about the exact model in the form…
Finite abstractions are discrete approximations of dynamical systems, such that the set of abstraction trajectories contains all system trajectories. There is a consensus that abstractions suffer from the curse of dimensionality: for the…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth…
To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…
In this paper, we study two variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian motions. One is the incomplete Taylor scheme which excludes…
We consider fast oscillating perturbations of dynamical systems in regions where one can introduce action-angle type coordinates. In an appropriate time scale, a diffusion approximation of the first-integrals evolution is described under…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Holder continuous solution. In case the diffusion is of order one or more, we obtain Holder estimates for the solution for any bounded drift. In…
This article develops and applies results, originally introduced in earlier work, for the existence of homotopy curves, terminating at a desired solution. We describe the principal hypotheses and results in section two; right inverse…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…
We describe a systematic approach [1] to the calculation of kinematic corrections ~ t/Q^2, m^2/Q^2 in hard exclusive processes which involve momentum transfer from the initial to the final hadron state. As an example, the complete…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general,…