Exercise 24.8 The object of this exercise is to indicate why the CIR model isconnected to squares of linear diffusions. Let Y be given as the solution to thefollowing SDE.dY = (2aY+o²) dt+20VYdW, Y(0) = 30.Define the process Z by Z(t) = √Y(t). It turns out that Z satisfies a sto-chastic differential equation. Which?

Given: Let Y be given as the solution to the following SDE, ,subjected to .Aim: To define the…

Answered: Exercise 24.8 The object of this…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A string of length L is secured at both ends. The string is released from rest with initial displacement f(x) at any point. Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. A. k- B. a A. 8²u D. 8:² 2²u მე:2 OM. dx li=0 du = J²u მე-2 Select ALL boundary/initial conditions that apply to this scenario du Otx=L du Du Ət 8x₂-0 du 3 8²u 0 0 Ət² = 0, 0 0 8²u dt² OB. = 0, t> 0 Ət 2-0 □c.u(0,t) = 0, t>0 du 0 0 7 dx \x-L = f(x), 00 H. (L, t) = 0, t> 0 1. u(a,0) = 0, 0 0 OL = 0, t> 0 = 0, t>0 = f(x), 0
The graph of F(y) vs y is as shown: y = -4 y = -3 y = -2 y = 4 y = 6 -6 y=8 -4 3- W We are trying to find and match the equilibrium solutions of the autonomous differential equation d dy F(y). In the below, match to the right dt correspondence. W= 1 2 F(y) 6 8 y Not a equilibrium point Not a equilibrium point Asymptotically Stable Semi Stable Not a equilibrium point Unstable ◄► ◄►
. Given the system of linear differential equations the nullclines and label the equilibrium point. di II Ax with A = [22]. construct
dz dy =2y +z and dx = 3y satisfies the relation dx Let k be real constant. The solution of the differential equations
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According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? Such a package is shown below, with and measured in inches. Assume . What are the dimensions of the package of largest volume? X y X Find a formula for the volume of the parcel in terms of and . Volume = cubic inches The problem statement tells us that the parcel's girth plus length may not exceed 108 inches. In order to maximize volume, we assume that we will actually need the girth plus length to equal 108 inches. What equation does this produce involving and ?
! Find a second solution y2(r) of the differential equation 22y" + 6xy' + 6y = 0, r>0, by the method of reduction of order given that yı(x) = is a solution of the equation. Compute the Wronskian and show that y1 and y2 are linearly independent.
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Vo) 4.5G 13:04 M LTE ll 88% Details The functions y1(t) = t² and y2(t) = t³ are solutions of the homogeneous differential equation t’y" – 4ty' + 6y = 0 on (0, ∞0). When using variation of parameters with y = u1(t)t² +u2(t)t³ to find a solution of the nonhomogeneous differential equation %3D t?y" – 4ty' + 6y = 4t°, what is the function u2(t) ? (Submit the corresponding number without parentheses.) (1) 4 (2) –4 (3) 4 (4) (5) -4t (6) –4t²
5) Consider the following mass-n-spring system. Let x(t) denote the displacement of the mass from its equilibrium. Write the differential equation for the damped oscillation, find x(t). (Zero external force.) k= 17 x(1)
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