Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}) and set (tau_{a}=inf left{s geqslant 0: B_{s}=aight}) where (a in

Question:

Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$ and set $\tau_{a}=\inf \left\{s \geqslant 0: B_{s}=aight\}$ where $a \in \mathbb{R}$. Show that $\tau_{a} \sim \tau_{-a}$ and $\tau_{a} \sim a^{2} \tau_{1}$.

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

Step by Step Answer:

Related Book For book-img-for-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 16, 2024 03:00 AM

See More Questions

In Problems 7 26, graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. x(t) = t - 3, y(t) = 2t+4; 0 < t < 2
In Problems 1 through 10, a matrix A is given. Use the method of Example 1 to compute A 5 . 1-3 0 2 0 0 1 0 2
In Problems 1 through 10, a matrix A is given. Use the method of Example 1 to compute A 5 . 4-3 -1 0 2 0 1 1 2
If an investor holds a credit-linked note and the credit event does not occur, the investor receives: A. All promised cash flows as scheduled. B. All coupon payments as scheduled but not the par...
What is the cause of Newton's rings?
See Table 2.5 showing financial statement data and stock price data for Mydeco Corp. Use the data from the balance sheet and cash flow statement in 2015 to determine the following: a. How much cash...
Mobile access to social media. The Marketing Management Journal (Fall 2014) published the results of a designed study to investigate satisfaction with the use of mobile devices to access social...
Brittany Adams contributed a patent, accounts receivable, and $61,000 cash to a partnership. The patent had a book value of $56,000. However, the technology covered by the patent appeared to have...
The controller of Hall Industries has collected the following monthly expense data for use in analyzing the cost behavior of maintenance costs. Month Total Maintenance Costs Total Machine Hours...
A $\mathbb{R}$-valued stochastic process $\left(X_{t}ight)_{t \geqslant 0}$ such that \(\mathbb{E}\left(X_{t}^{2}ight)
Show that (B1) is equivalent to Bt-Bs for all 0 < s < t.
Express the number in scientific notation. 1,260,000,000
How do these relevant legal principles apply: Duty of care Duty of obedience Duty of loyalty Shareholder Derivative suit Piercing the corporate veil...
what will you do as a hotel manager if a customer complained about bad service they received?
How do marketers use new products to maintain and grow their market share? Your response must include a specific example of a company that successfully grew its business or attracted a new target...
How do you encourage cross-functional synergy within your organization to break down silos and facilitate innovative solutions to complex challenges ?
1. what is intended internal resource strategies. How do you plan to develop or acquire resources (tangible and/or intangible) that would generate core competencies? What are examples of resource...
Let X 1 , . . ., X n be a random sample from an exponential population with parameter .
Ask students to outline the reasons why the various elements of culture (social structures and control systems, language and aesthetics, religion and other belief systems, educational systems, etc.)...
Two dice are rolled. Let X and Y be the numbers appeared; and events A = {X is even}, B = {X+Y is even}, A = {X is divided by 4}, B = {X+Y is divided by 4}. Check for independence the pairs A, B and...
Two cards are selected at random from a deck of 52. Guess whether the events A 1 = {at least one card is a king}, A 2 = {at least one card is an ace} are independent. Justify your guess rigorously.
(a) Consider two singletons, [ 1 ] and [ 2 ]; that is, events containing only one outcome each. Are they independent? (b) Are disjoint events independent? (c) Let P(A 1 ) = P(A 2 ) = 1. Are A 1 ,A 2...
What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $967.00? That sells for $1,206.10?
1)Prepare the journal entry to record Tamas Companys issuance of 6,500 shares of $100 par value, 9% cumulative preferred stock for $105 cash per share. 2. Assuming the facts in part 1, if Tamas...
On consolidated financial statements, where does the parents equity in the net income of the subsidiary account appear? A. On the consolidated income statement, as a revenue B. On the consolidated...

Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}) and set (tau_{a}=inf left{s geqslant 0: B_{s}=aight}) where (a in

Question:

Step by Step Answer:

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

Students also viewed these Business questions