Let (left(u_{n}, mathscr{A}_{n}ight)_{n in mathbb{N}}) be a supermartingale and (u_{n} geqslant 0) a.e. Prove that (u_{k}=0) a.e.

Question:

Let $\left(u_{n}, \mathscr{A}_{n}ight)_{n \in \mathbb{N}}$ be a supermartingale and $u_{n} \geqslant 0$ a.e. Prove that $u_{k}=0$ a.e. implies that $u_{k+n}=0$ a.e. for all $n \in \mathbb{N}$.

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

Step by Step Answer:

Related Book For answer-question

Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

See More Books

Question Posted: Jan 25, 2024 01:05 AM

See More Questions

Let E1 be the unit interval [0, 1] with its middle third (1/3, 2/3) removed (i.e., E1 = [0, l/3]U[2/3, 1]). Let E2 be E1 with its middle thirds removed; that is, E2 = [0, 1/9] U [2/9, 1/31 U [2/3,...
Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
Let E be a set in Rm. For each u: E R which has second-order partial derivatives on E, Laplace's equation is defined by a) Show that if u is C2 on E, then Îu = (u) on E. b) Show that if E R3...
What is the advantage of using computing to simulate an automobile crash test as opposed to actually staging a crash?
If the principal quantum number n were limited to the range from 1 to 6, how many elements would we find in nature?
When selecting a food delivery system, which of the following factors is most important in relation to the microbial quality of delivered food? A. Labor skills B. Form of food purchased C. Time span...
Briefly discuss the strengths and limitations associated with this approach and the specific design . Develop a hypothetical research scenario that would necessitate the use of the Action Research...
Angela Lansbury Company deposits all receipts and makes all payments by check. The following information is available from the cash records. Instructions (a) Prepare a bank reconciliation going from...
Consider the Solow model we studied in class, with the production function given by: Y =AKN1. tttt In this question, we distinguish between the labor force (L) and the total population (Pop). The...
Verify that the family $\mathscr{A}_{\tau}$ defined in Definition 23.5 is indeed a $\sigma$-algebra. Data from definition 23.5 Definition 23.5 Let (X, A, An, ) be a o-finite filtered measure...
Let $(X, \mathscr{A}, \mu)$ be a $\sigma$-finite measure space, let $u$ be a further measure on $\mathscr{A}$ and let $\left(A_{n, i}ight)_{i \in \mathbb{N}} \subset \mathscr{A}$ be for...
Does the outcome in this case underscore the advantages or the disadvantages of the limited liability company form of business organization? Explain.
The current gain of a BJT operating at a collector current of 16.8 mA is 200. Calculate its input resistance. Give your answer in k and round it to three decimal places.
Radio station WBAB in Babylon broadcast at a frequency of 102.3 MHz. What is the wavelength of the radio wave emitted by WBAB?
The sampling distribution of the sample mean is shown. If the sample size is n = 25, what is the standard deviation of the population from which the sample was drawn? Round to the nearest thousandth...
Reflect on the different accounting methods for investments and their impact on the financial statements of companies. How do these methods affect the portrayal of a company's financial health and...
M N P R S T Find the value at retirement using the information below. Payments are scheduled at the end of the period. Afterwards, create a two variable data table to find the different retirement...
Washoe Medical Center, Inc., admitted Shirley Swisher for the treatment of a fractured pelvis. During her stay, Swisher suffered a fatal fall from her hospital bed. Gerald Parodi, the administrator...
For the following exercises, write the polynomial function that models the given situation. Consider the same rectangle of the preceding problem. Squares of 2x by 2x units are cut out of each corner....
How does building new systems produce organizational change? a. Describe each of the four kinds of organizational change that can be promoted with information technology. b. Define business process...
What are the core activities in the systems development process? a. Distinguish between systems analysis and systems design. Describe the activities for each. b. Define information requirements and...
What are alternative methods for building information systems? a. Define the traditional systems lifecycle. Describe its advantages and disadvantages for systems building. b. Define information...
How would you address high conflict and low productivity in a team using organizational behavior principles?
How do information systems contribute to the efficiency and effectiveness of organizations, and what role do they play in decision-making processes?
On February 1 5 , Alpha Inc purchased 3 6 , 0 0 0 common shares of Beta Corp. at $ 3 0 each, plus transaction costs totaling $ 9 , 0 0 0 . During the year, Beta Corp. paid a dividend of $ 1 . 2 5 per...

Let (left(u_{n}, mathscr{A}_{n}ight)_{n in mathbb{N}}) be a supermartingale and (u_{n} geqslant 0) a.e. Prove that (u_{k}=0) a.e.

Question:

Step by Step Answer:

By definition a supermartingale satis...View the full answer

Measures Integrals And Martingales

Students also viewed these Business questions