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Oct
15
awarded  Yearling
Oct
15
comment A question on semi-martingale and its variations
Poisson process is a semimartingale. Generally, a semimartingale can be represented as a sum of a local martingale and a finite-variation process. This the Bichteler-Dellacharie theorem: almostsure.wordpress.com/2011/03/28/…
Oct
15
revised A question on semi-martingale and its variations
added 1 character in body
Oct
15
answered A question on semi-martingale and its variations
Oct
15
comment Zero mean but not a martingale
Also, an example of a stationary martingale is the constant process $X$ with $X_t = 0$.
Oct
15
comment Zero mean but not a martingale
The last sentence is not correct. Standard Brownian Motion $(B_t)_{t\geq 0}$ is a martingale with $E B_t = 0$ for all $t$.
Oct
13
comment Problems about the upcrossing lemma.
$H_4=1$ because $X_3<a$ and we start investing. But $H_4$ is set at time $n=3$.
Oct
13
comment Problems about the upcrossing lemma.
Profit at time $n$ is $H_n ( X_n - X_{n-1})$, and $H_n$ is the amount traded at time $n-1$. $H_n$ is previsible and therefore known at time $n-1$.
Oct
11
answered Showing a sequence of Random Variables (Submartingale) Converges.
Oct
10
comment Showing a sequence of Random Variables (Submartingale) Converges.
Are you sure, we don't have $E \sum Y_n < \infty$?
Apr
28
awarded  Popular Question
Nov
19
comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen?
You put 3 pigs into first 3 pens, and remaining 6 pigs into the fourth pen. Then you crawl into the fourth pen.
May
15
awarded  Caucus
Mar
11
comment What are $C_b^2 (\mathbb R)$ and $C^{2,1} (\mathbb R × \mathbb R^+ )$?
What are the functions $a$ and $b$ for?
Mar
10
answered Stochastic processes for beginers (good links and books)
Jan
29
comment see when two measures are equal on σ-algebra generated by all intervals in [a,b].
Monotone Class Theorem is perhaps a more common name for Dynkins's lemma mentioned by @gnometorule
Jan
27
comment Approximation of SDE
A nice book covering simulation of SDEs is Iacus: Simulation and Inference for SDEs. In particular you will find the formulas for exact simulation for most popular models.
Nov
6
comment general semimartingale theory
You may also try the book "Stochastic integration with jumps" by K. Bichteler. It has a lot of exercises. A version of the book is available on authors' homepage..
Sep
20
comment Limit of series
Javaman's statement is also correct :)
Aug
1
awarded  Critic