Analysis of piecewise linear stochastic systems in half-spaces by means of the Pugachev-Sveshnikov equation

Zayats Oleg I.

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Analysis of piecewise linear stochastic systems in half-spaces by means of the Pugachev-Sveshnikov equation

机译：通过Pugachev-Sveshnikov方程分析半空间中分段线性随机系统的分析

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An analytic approach is presented to obtain a probability distribution function of the state-vector of piecewise linear systems which have two domains (half-spaces) of linearity. The approach is based on the use of the Pugachev – Sveshnikov equation for the characteristic function and its reduction to the parametric Riemann boundary value problem for half-planes. Crandall’s problem for anisotropic viscosity friction is solved as an example of application of the derived theory. The displacement of a body, placed on a randomly oscillating foundation, is explored. And the asymptotical behaviour of the mathematical expectation of this body’s displacement is obtained.

机译：提出了一种分析方法以获得具有两个域（半空间）的线性度的分段线性系统的状态矢量的概率分布函数。该方法基于Pugachev - SVeshnikov方程的特征函数的使用及其对参数riemann边值问题的半平面。 CrandAll对各向异性粘度摩擦的问题是解决了衍生理论的应用的例子。探讨了在随机振荡基础上的身体的位移。获得了这种身体位移的数学期望的渐近行为。

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《St. Petersburg Polytechnic University Journal: Physics and Mathematics》 |2013年第4期|共15页
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Zayats Oleg I.;
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continuous Markov processPugachev – Sveshnikov equationRiemann boundary value problemstochastic mechanicsCrandall’s problemanisotropic viscous friction;

机译：连续马尔可夫Processpugachev - Sveshnikov公式riemann边值问题有问题的机械臂的有问题的粘性摩擦摩擦;

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2. General linear quadratic optimal stochastic control problems with random coefficients: Linear stochastic Hamilton systems and backward stochastic Riccati equations [J] . Tang SJ. SIAM Journal on Control and Optimization . 2003,第1期

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8. PLALGO: A FORTRAN Implementation of a Piecewise-Linear Homotopy Algorithm for Solving Systems of Nonlinear Equations [R] . Todd, M. J. 1980

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Analysis of piecewise linear stochastic systems in half-spaces by means of the Pugachev-Sveshnikov equation

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