相关论文: Analytical solution for multivariate statistics in…
We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
Analytical periodic solutions for weakly Coupled Map Lattices are shown in an explicit form as well as in a recurrence relation. The results establish a link between a matricial representation and recurrence relations of the solutions.
In this paper we study random optimization problems where random functions are investigated in sample paths. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
We present a multivariate one-sided sensitivity analysis for matched observational studies, appropriate when the researcher has specified that a given causal mechanism should manifest itself in effects on multiple outcome variables in a…
In this paper, we introduce an analytical perturbative solution to the Merton Garman model. It is obtained by doing perturbation theory around the exact analytical solution of a model which possesses a two-dimensional Galilean symmetry. We…
We study the autonomous systems of quadratic differential equations of the form $\dot{x}_i(t)=\mathbf{x}(t)^T \mathbf{A}_i \mathbf{x}(t) + \mathbf{v}_i^T \mathbf{x}(t)$ with $\mathbf{x}(t) = (x_1(t),x_2(t),\dots,x_i(t),\dots)$ which, in…
This work considers the allocation problem for multivariate stratified random sampling as a problem of integer non-linear stochastic multiobjective mathematical programming. With this goal in mind the asymptotic distribution of the vector…
Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results…
We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability…
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…