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We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent SDEs containing running…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
The discrete ordinates method with angular parameters is discussed in light of the recent extension of its underlying hypothesis. The analysis shows that the method, although it compares very well with the trajectory of photons model, it…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…
We obtain estimates on the continuous dependence on the coefficient for second order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and Gripenberg to…
The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for…
The problem of individualized prediction can be addressed using variants of conformal prediction, obtaining the intervals to which the actual values of the variables of interest belong. Here we present a method based on detecting the…
We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
In this article, we introduce a new class of coupled fractional Lane-Emden boundary value problems. We employ a novel approach, the fractional Haar wavelet collocation method with the Newton-Raphson method. We analyze the conditions in two…
We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences…
Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…
In this paper we propose some approaches for finding of pointwise estimates of a solution of the Dirichlet boundary value problem $-\Delta u \pm |u|^{q-1} u = 0 $, $|u|=k$ when $|x|=d<1$ and $|u|=0$ when $|x|=1$ where $x\in \Omega = \{x|…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.