Related papers: Stochastic solutions of nonlinear pde's: McKean ve…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…
For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic…
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…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
The distribution-dependent stochastic differential equations (DDSDEs) describe stochastic systems whose evolution is determined by both the microcosmic site and the macrocosmic distribution of the particle. The density function associated…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
In this work we review the basic principles of stochastic logic and propose its application to probabilistic-based pattern-recognition analysis. The proposed technique is intrinsically a parallel comparison of input data to various…
In this work we study the problem of constructing stochastic processes with a predetermined covariance decay by parameterizing its marginals and a given family of copulas. We show that the proposed methodology is compatibility-free and…
Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
A method to construct the exact solution of the PDE is presents, which combines the two kind methods(the nonlinear transformation and RQ(Reduction the PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen to…
McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of…
The syntactic nature and compositionality characteristic of stochastic process algebras make models to be easily understood by human beings, but not convenient for machines as well as people to directly carry out mathematical analysis and…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…
In the first part of the paper we develop the sensitivity analysis for the nonlinear McKean-Vlasov diffusions stressing precise estimates of growth of solutions and their derivatives with respect to the initial data, under rather general…
Stochastic linearization is a method used in Quasilinear Control (QLC) to replace a nonlinearity by an equivalent gain and a bias, utilizing the statistical properties of random inputs. In this paper, the theory of stochastic linearization…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…