Assume that X(t) and Y(t) are two independent standard Brownianmotion processes satisfying X(0) = 0 and Y(0) = 0. Let M(t) = max0 z, X(t) ≤ x) = 1 − Þ·0 (22-72),z > 0, x 0.[Hint: Apply Reflection Principle for (i).]

Part (ii) Find the joint probability density function, fM(t),X(t)(z,x), of M(t) and X(t) for t >…

Answered: Assume that X(t) and Y(t) are two…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

See similar textbooks

Similar questions

Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.
13 Find the linearizatan 2=L(x.y) f the function 2= {(x,y)=4x²-y²+2y at the point (x.y) = (3,2).
1. For the LTI ODE x(t) + 3x(t) +9x(t) + 14x(t) = u(t) a) Derive the transfer function if y(t) = 2x(t) + 3x(t) b) Based on the transfer function you derived, find the poles and zeros of the transfer function c) Use the initial value theorem to find the instantaneous change in y if a step input u = 1 is applied to the system at rest at t = 0 d) Use the final value theorem to find the steady-state value of y if a step input u = 1 is applied to the system at rest at t = 0 e) Convert the LTI ODE into state space in Matlab f) Use step to confirm your answers in parts (c) and (d) g) Use ss2tf to confirm your answer to part (a) h) Use roots on your results from ss2tf to confirm your answer to part (b) i) Also use eig to confirm the poles in part (b)
#11 help
Exercise 3. A WSS process X(t) with autocorrelation function Rx(+) = e-2/(207) is passed through an LTI system with transfer function H(w) = e-w²/(20). Denote the system output by Y(t, Find (a) Sxy(w) (b) RXY (T) (c) Sy (w) (d) Ry (T)
Find the nullity of T. T: R* - R2, rank(T) = 2 nullity(T) =
Solve for pt
Find the equilibrium points of d = y²(6 - y)² and classify each one as stable, unstable, or dt semistable. Stable equilibria occur at y = Unstable equilibria occur at y = Semistable equilibria occur at y = (If there is more than one equilibrium of a certain type, enter a comma-separated list. If there are no equilibria, enter "none".) On paper, sketch several solutions to the differential equation.
7. For what points (xo,Yo) does Theorem A imply that the initial value problem y' =y\y\, _y(x)=y, has a unique solution on some interval |x – xo|

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Assume that X(t) and Y(t) are two independent standard Brownian motion processes satisfying X(0) = 0 and Y(0) = 0. Let M(t) = max0 z, X(t) ≤ x) = 1 − Þ ·0 (22-72), z > 0, x 0. [Hint: Apply Reflection Principle for (i).]