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bio website wergieluk.com
location Germany
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visits member for 4 years, 4 months
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Dec
9
comment Notation for intersection of functions
Yes, but the question is, is there an established notation / symbol for that? Something like $f \cap g$.
Dec
9
comment Probability of a zero product given one previous zero product
$v$ and $w$ have different dimensions and their inner product is not well-defined.
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
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 $n-1$.
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.
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?
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 :)
Jan
13
comment Exercises for “Limit Theorems for stochastic processes”
Jacod&Shiryaev is not a textbook. This is why there are no exercises in it. Are you sure, this book is suitable for your needs?
Dec
10
comment How is the law of a stochastic process defined?
The second construction is called "finite-dimensional distributions". Wikipedia is perhaps not the best place to learn about this.. I would recommend reading the first two chapters of this lecture notes: stat.cmu.edu/~cshalizi/754
Nov
30
comment Confidence band for Brownian Motion with uniformly distributed hitting position
Note that the second requirement was that, the hitting time of the boundary is uniformly distributed on $[0,1]$. Can you prove this for $u(t)=c^*$?
Nov
30
comment Confidence band for Brownian Motion with uniformly distributed hitting position
Sorry guys! I missed that interesting discussion in March. I particularly like the discretization idea. The method could give us the idea how such a curve might look like. Thanks!
Nov
28
comment Exercises on stochastic calculus
Small hint: solutions to the exercises from the first three chapters of Protters book are available on his homepage.
Nov
27
comment Is this some type of convergence of stochastic processes?
As far as I know the above is just the $L^2(dP,dt)$ convergence. Other type of convergence used for constructing stochastic integrals is for example ucp convergence. Protter is a good reference on that.
Nov
14
comment Double exponential distribution is not an exponential family
@cardinal Thanks for your comments! I should have mentioned I'm interested in a special case with one-dimensional $\xi$ and $T$.