Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (int_{0}^{T} B_{s}^{2} d B_{s}=frac{1}{3} B_{T}^{3}-int_{0}^{T} B_{s} d s,

Question:

Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Show that $\int_{0}^{T} B_{s}^{2} d B_{s}=\frac{1}{3} B_{T}^{3}-\int_{0}^{T} B_{s} d s, T>0$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

ISBN: 9783110741254

3rd Edition

Authors: René L. Schilling, Björn Böttcher

See More Books

Question Posted: Mar 17, 2024 01:00 AM

See More Questions

Determine if the given expression approaches a limit as b , and find that number when it does. 1 b 3
In Problem find the transpose of each matrix. 1 2 -1 2 -7 8 1 4 -1 3
Solve each equation in Exercises 83108 by the method of your choice. 1 X + 1 x + 2 1 3
A company has the following data: net sales, $405,000; cost of goods sold, $220,000; selling expenses, $90,000; general and administrative expenses, $60,000; interest expense, $4,000; and interest...
In each of Exercises 1-3, determine whether r is positive, negative, or zero. 1. 2. 3.
End A of the 6-kg uniform rod AB rests on the inclined surface, while end B is attached to a collar of negligible mass which can slide along the vertical rod shown. Knowing that the rod is released...
Consider the following cash flow profile and assume MARR is 10 percent/year. a. What does Descartes' rule of signs tell us about the IRR(s) of this project? b. What does Norstrom's criterion tell us...
Tanek Industries manufactures and sells three different models of wet-dry shop vacuum cleaners. Although the shop vacs vary in terms of quality and features, all are good sellers. Tanek is currently...
If an employee's benefit is paid from a qualified plan in the form of a qualifying lump-sum benefit at retirement, the employee's cost basis will be recovered _______________ with an income tax...
Let $\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}$ be a one-dimensional Brownian motion, \(T
Let $\left(X_{n}ight)_{n \geqslant 0}$ be a sequence of r. v. in $L^{2}(\mathbb{P})$. Show that $L^{2}-\lim _{n ightarrow \infty} X_{n}=X$ implies \(L^{1}-\lim _{n ightarrow \infty}...
Arthur Castle is interested in identifying the average number of family members living in each household in his neighborhood. He has heard about sampling and thinks that it could help him identify...
A digital 11R felter block diagram shown in figure a) Find the trans for function H(Z) in transfer b) Find the range stable, if gain c) Realize the terms of a and b of and b to keep the filter is...
Decorative Designs (DD) is a family-owned furniture manufacturing company in Vietnam established in January 2015. The CEO of the company met a financial consultant recently to obtain some financial...
Superin Calculate the current price of Patience, Inc. stock that is expected to pay a dividend of $4/share at the end of each year from year 33 through year 61, given a discount rate of 5%. This...
Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rf. The characteristics of two of the stocks are as follows: StockExpected Return Expected...
In a 15 TR ammonia refrigeration plant, the condensing temperature is 25C and evaporating temperature -10C. The refrigerant ammonia is sub cooled by 5C before entering through the throttle valve. The...
Suppose you are looking along a line through the centers of two circular (but separate) wire loops, one behind the other. A battery is suddenly connected to the front loop establishing a clockwise...
The following cost information was provided to you for analysis: September 12,000 Units Produced Costs: TIC TAC TOE TING August 10,000 P80,000 70.000 60.000 50,000 How much is the fixed cost per...
Let w t1 and w t2 be independent Brownian motions. Find for which the process w t1 +2w t2 has the same distribution as w t1 .
Let wt be Brownian motion. (a) Are w 1 and w 5 independent r.v.s? (b) Answer the same question for w 1 and w (1,5] . (c) Find P(w 1 +w 5 < 4).
Provide an Excel worksheet illustrating the invariance principle of Section 1.1.2. To do this, simulate values of some independent r.v.s, for example, exponential or uniform, construct sums S k , and...
Have you heard of "The Five Forces model" popularized by Harvard professor Michael Porter, that is a framework for analyzing the attractiveness of an industry? These readings came from the book...
How did Cristiano Schena and his team at Caterpillar Brazil use employee engagement and motivation to turn around a struggling business unit? What role did this approach play in sustaining the...
Technology has brought about many changes. Global learning experiences can also bring about change. In a recent study the author stated: "Regarding global learning, specifically, they became more...

Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (int_{0}^{T} B_{s}^{2} d B_{s}=frac{1}{3} B_{T}^{3}-int_{0}^{T} B_{s} d s,

Question:

Step by Step Answer:

Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

Students also viewed these Business questions