Convergence Of Random Variables Sequences In Sublinear Expectation Theory And Application Of Sublinear Expectation To The Wave Equation

This paper is mainly divided into two parts,which mainly solve the problem of convergence of random variable sequences in sublinear expectation space and the application of sublinear expectation in partial differential equations.The first part reconsiders the random variables sequence sublinear expectation p step convergence definition through the angle of distance space.We compares the definition of infinite norm convergence to show that if the sequence of random variables converges according to the infinite norm,then it must also convergence as sublinear expectation 1 step.At the same time,the author also shows that if the sequence of random variables satisfy sublinear expectation p step convergence,then the sequence can also be deduced to converge by distribution.Then,we introduces the convex theorem proposed by Pollar.At the same time,combining the convex theorem and the convexity of sublinear expectations,we give two inferences and proof them.The second part mainly writes about the sublinear expectation distribution,the application of sublinear expectation as a viscous solution of a partial differential equation to a specific solution to the equation.We give the specific cases that the definitions of the two-dimensional maximum distribution and the G-normal distribution,and proves the distribution problem of two one-dimensional random variables combining into twodimensional random variables.Since the sublinear expectation of maximum value distribution is a sticky solution of a one-dimensional partial differential equation,we introduce expectation and sublinear expectation into the process of solving the wave equation,and gives a special form of solution to the wave equation.Finally,the author derives the twodimensional Laplace equation from the G-heat equation of the two-dimensional G-normal distribution,and give the consideration of the sublinear expected distribution.