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Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…
We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length…
Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on the space of square-integrable functions, whose…
The problem of continuous data assimilation for semilinear parabolic equations based on partial observations corrupted by noise is investigated. The noise is allowed to be multiplicative, with additive noise arising as a special case. In a…
We show that translations and dilations of a p-adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p-adic wavelets. In this sense the continuous p-adic wavelet transform…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
Bayesian inference with empirical likelihood faces a challenge as the posterior domain is a proper subset of the original parameter space due to the convex hull constraint. We propose a regularized exponentially tilted empirical likelihood…
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
A naive theory of additive perturbations on a continuous probability distribution is presented. We propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the…
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based…