610hw3

# 610hw3 - FE 610 Homework 3 Lena Yemelyanov Due Wednesday...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FE 610 Homework 3 Lena Yemelyanov Due: Wednesday, November 8, 2009 The Full Assignment is from PDF available online Question 1 : Problem statement : Differentiate the following functions with respect to the Wiener process W t , and if applicable, with respect to t. (a) f W t W t 2 f W t W t Solution for ( a ): dF W t , t F s dW t F t dt 1 2 F ss dt F s- first derivative of the innovation term F ss- second derivative of the innovation term F t- first derivative of teh drift term f W t W t 2 F s dW t 2 W t dW t Since our f W t does not have a drift term F t dt 1 2 F ss dt 1 2 ∗ 2 ∗ dt dt f ′ W t dt 2 W t dW t The second problem is solved in a similar manner as the problem above, since the only difference is the exponent. f W t W t W t 1/2 F s dW t 1 2 W t − 1/2 dW t dW t 2 W t F t dt 1 2 F ss dt 1 2 ∗ 1 2 ∗ − 1 2 ∗ W t − 3/2 dt − 1 8 W t − 3/2 dt f ′ W t − 1 8 W t − 3/2 dt 1 2 W t − 1/2 dW t Problem statement ( b ): f W t e W t 2 Solution ( b ): 1 dF W t , t F s dW t F t dt 1 2 F ss dt F s dW t 2 W t e W t 2 dW t F t dt 1 2 F ss t 2 dt 1 2 2 e W t 2 4 W t 2 e W t 2 dt e W t 2 dt 2 W t 2 e W t 2 dt dF W t , t e W t 2 2 W t 2 e W t 2 dt 2 W t e W t 2 dW t Problem statement ( c ): f W t , t e W t − 1/2 2 t f W t , t e W t Solution ( c ): f W t , t e W t − 1/2 2 t dF W t , t F s dW t F t dt 1 2 F ss dt F s dW t e W t − 1/2 2 t dW t F t dt − 1 2 2 e W t − 1/2 2 t dt 1 2 F ss dt 1 2 2 e W t − 1/2 2 t dt dF W t , t e W...
View Full Document

## This note was uploaded on 02/27/2010 for the course FE 610 taught by Professor Prasad during the Spring '10 term at Stevens.

### Page1 / 8

610hw3 - FE 610 Homework 3 Lena Yemelyanov Due Wednesday...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online