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(i) Show the SDE dX₁ = µX₁d₁ + X³¹dB, has the uniqueness or not, where μ is constant. (ii) For any opend-interval (a, b), the function f(x) which satisfies local-lipschitz condition is defined as the existence of the positive-constant(depend on a, b) Ka, b it holds: For Vx, y > 0, |f(x) = f(y)| ≤ Ka, blx – yl.*1 Show it satisfies local-lipschitz condition if the function f(x) is the class C¹ function. [Hint) Use a property (Theorem) for continuous func. we learned at calculus.

(i) Show the SDE dX₁ = µX₁d₁ + X³¹dB, has the uniqueness or not, where μ is constant. (ii) For any opend-interval (a, b), the function f(x) which satisfies local-lipschitz condition is defined as the existence of the positive-constant(depend on a, b) Ka, b it holds: For Vx, y > 0, |f(x) = f(y)| ≤ Ka, blx – yl.*1 Show it satisfies local-lipschitz condition if the function f(x) is the class C¹ function. [Hint) Use a property (Theorem) for continuous func. we learned at calculus.

Advanced Engineering Mathematics
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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μ (i) Show the SDE dX₁ = µX₁d₁ + X¾³¹dB₁ has the uniqueness or not, where µ is constant. (ii) For any opend-interval (a, b), the function f(x) which satisfies local-lipschitz condition is defined as the existence of the positive-constant(depend on a, b) Ka, b it holds: For Vx, y > 0, f(x) = f(y)| ≤ Ka, blx - yl.*¹ Show it satisfies local-lipschitz condition if the function f(x) is the class C¹ function. 【Hint】 Use a property (Theorem) for continuous func. we learned at calculus.
Transcribed Image Text:μ (i) Show the SDE dX₁ = µX₁d₁ + X¾³¹dB₁ has the uniqueness or not, where µ is constant. (ii) For any opend-interval (a, b), the function f(x) which satisfies local-lipschitz condition is defined as the existence of the positive-constant(depend on a, b) Ka, b it holds: For Vx, y > 0, f(x) = f(y)| ≤ Ka, blx - yl.*¹ Show it satisfies local-lipschitz condition if the function f(x) is the class C¹ function. 【Hint】 Use a property (Theorem) for continuous func. we learned at calculus.
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