ﻻ يوجد ملخص باللغة العربية
If the coefficients of polynomials are selected by some random process, the zeros of the resulting polynomials are in some sense random. In this paper the author rephrases the above in more precise language, and calculates the joint conditional densities of a random vector whose values determine almost surely the zeros of a random reduced cubic.
We consider random polynomials whose coefficients are independent and uniform on {-1,1}. We prove that the probability that such a polynomial of degree n has a double root is o(n^{-2}) when n+1 is not divisible by 4 and asymptotic to $frac{8sqrt{3}}{
We prove the existence and uniqueness for SDEs with random and irregular coefficients through solving a backward stochastic Kolmogorov equation and using a modified Zvonkins type transformation.
It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada-Watanabe theorem cite{yamada1,yamada2} and the Feller test for explosions cite{
The aim of this paper is to obtain convergence in mean in the uniform topology of piecewise linear approximations of Stochastic Differential Equations (SDEs) with $C^1$ drift and $C^2$ diffusion coefficients with uniformly bounded derivatives. Conver
We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary ergodic in time. As was proved in [24] and [12] in this case the homog