Question: Exercises 2.3 Wick's identity Let Wt be a Brownian motion. 1. Prove that EP[eiuWt ] = e????u2t 2 2. Deduce the following formula, called the

Exercises 2.3 Wick's identity Let Wt be a Brownian motion.

1. Prove that EP[eiuWt ] = e????u2t 2

2. Deduce the following formula, called the Wick identity, 8n 2 N EP[(Wt)2n] =

(2n ???? 1)!

2n????1(n ???? 1)! tn EP[(Wt)2n+1] = 0

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Financial Modeling Questions!

Q:

where the polynomial and 2.13 are the section 2.1 is about the Adams method 2.3 Instead of (2.3), consider the identity g(tnes) = g(tnes-2)+ f(t,y(T)) dr. tnts-2 a Replace f(t, y(1)) by the...

Q:

I need help with the following questions. I have attached them below. Given any real number, there is a real number that is greater. Given any real number r , there is ____ s such that s is _____....

Q:

10. [0.09/0.27 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.4.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER "Unknown cultural affiliations and loss of identity at high elevations." These are...

Q:

Can You answer all of these questions? 2.2 Venn Diagrams and Subsets 65 HW # 1-6 all # 41, 43, 47, 49, 53 7- 13odd 15-21 odd 2 EXERCISES 23 - 29 odd Match each set or sets in Column I with the...

Q:

758 CHAPTER 14 CALCULUS OF VECTOR-VALUED FUNCTIONS . If R', (t) = R'2(t), then Ri(t) = R2(f) + c for some constant vector c. . The Fundamental Theorem of Calculus for vector-valued functions: If r()...

Q:

For IE! Exercises 17. 20, refer to vectors v and w in the gure. Cb J '01 \" . a. Sketch v + w by placin ' e initial point of W at the terminal point of v. I). Sketch V ' - by drawing v and w with the...

Q:

Take this test as you would take a test in dass. After you are finished, check your work against the answers given in the back of the book. L. If tan of 3 : and cos & - 0, use the fundamental...

Q:

In Exercises 21 and 22, write the statement as a power function equa- tion, Let k be the constant of variation. 22. The force of gravity F acting on an object is inversely propor- tional to the...

Q:

Lab 3 Managing Linux Permissions Complete the following exercises, making sure to follow the instructions carefully. Dont forget to put your name in the top right-hand corner of this document and...

Q:

30. 6x - Sy - 30 31. y - -2x + 3 32 y = -3x + 1 - 2 33. Concept Check Consider the patterns formed in the tables for Exercises 23 and 31. Fill in each blank with the appropriate number. () In...

Q:

You have an array A of size N [divisible be 3] populated with unique values. You have divided this array into three equal parts and every part is in sorted order that can be ascending or descending....

Q:

Posse Corporation plans to form a foreign subsidiary through which to conduct a new business in Country J. Posse projects that this business will operate at a loss for several years. a. To what...

Q:

Which of the following statements is CORRECT? a . The longer the time to maturifg. the smaller the change in the valur of a bond in response to a given changr in ingerest races. b . You hold two...

Q:

How much should you deposit in an account paying 8% compounded quarterly in order to receive quarterly payments of $1,000 for the next 4 years?

Q:

You are offered an asset costing $600 that has cash flows of $100 at the end of each of the next 10 years. a. If the appropriate discount rate for the asset is 8%, should you purchase it? b. What is...

Q:

You are offered an asset costing $600 that has cash flows of $100 at the end of each of the next 10 years. a. If the appropriate discount rate for the asset is 8%, should you purchase it? b. What is...

Q:

You just took a $10,000, 5-year loan. Payments at the end of each year are flat (equal in every year) at an interest rate of 15%. Calculate the appropriate loan table, showing the breakdown in each...

Q:

13) At the maturity of an issued bond, the company who issued the bond must pay the A) face value B) future value C) discounted value D) premium value E) none of the above

Q:

Analyst forecasts of earnings per share (EPS) and dividends per share (DPS) for IMD Ltd. over the next two years are as follows: 2022 E 2023 E EPS = $10.00 EPS = $11.00 DPS = $2.00 DPS = $2.25...

Q:

Exercise 1-4 (Algo) Fixed and Variable Cost Behavior [LO1-4] Espresso Express operates a number of espresso coffee stands in busy suburban malls. The fixed weekly expense of a coffee stand is $1,500...