All Questions

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About the boundary conditions of the Black-Scholes-Merton PDE

I have a question about the solution of the Black-Scholes PDE for the European call option when I read the book Stochastic Calculus for Finance II of Steven E.Shreve. Let $c(t,x)$ be the value of the ...
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Let $A$ be a (finitely generated) free group and $G$ be a (finitely generated) free $A$-group - that is, a group with an action of $A$, which is free in the category of groups with an $A$-action. ...
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Intuition behind the Morse inequalities?

Forgive me if this is sort of a vague question, but can someone supply me with their intuition behind the Morse inequalities?
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Systems of stochastic differential equations with non-Lipschitz coefficients

I am looking for references to any literature which might consider the existence / behavior / regularity of solutions to systems of stochastic differential equations with non-Lipschitz coefficients. ...
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Permutation equivalence classes with kendall-tau distance

I asked this question on Stack Exchange a few days ago with no help. I am not sure if the question seems too trivial or of not enough general interest to get any attention. Anyway, any sort of ...
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Is there a structure theorem or group law for finite groups generated by two elements?

Say that $a, b \in G$ are two elements of a finite group $G$. Is there a structure theorem for the structure of $\langle a,b\rangle$? Is there a way to derive group laws for the group operation in the ...
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Relation between moduli spaces and classifying spaces

I hope this question is suitable to be posted here on MO. I wonder if there is a systematic relation between the notation of a classifying space, and the notion of a moduli space. I don't consider ...
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Number of bases of a matroid

I would like to know the minimum number of bases of a matroid of rank $k$ and $n$ elements, knowing that each singleton is independent. At least for small ranks.
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Distribution of Poles of solutions to the first Painleve equation

In the introduction of this paper the distribution of the poles of solutions to the first Painlevé equation is discussed. In particular it is said that the poles form a deformed lattice that ...
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Maximal opening angle of a polygon from a point [on hold]

I'm looking for an algorithm that given a 2D convex polygon and point outside it, returns the two points of the polygon which are the two extremities of the polygon when viewed from that point. One ...
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Norm inequalities between difference operators

Assume $(v_i)$ to be a sequence in $\ell_\infty(\mathbb{R})$ for $i=1,\dotsc,N$. Define the difference operator as $\Delta v_i:=v_{i+1}-v_i$ and $\Delta^n v_i:=\Delta(\Delta^{n-1} v_i)$. Then, how can ...
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Distribution of $\sin(X) *\cos(Y)$ where $X,Y$ are iid r.v., uniformly distributed on $[0, 2 \pi]$ [migrated]

What is the probability density of $R = \sin(X) * \cos(Y)$ where $X,Y$ are independent random variables, uniformly distributed on $[0, 2 \pi]$? I am stuck with complicated integrals, not sure if ...
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Space of polynomially growing harmonic functions on a Lie group

There is a recent theorem by Kleiner (based on previous work by Colding & Minicozzi), that reads: If $G$ is a finitely generated group of polynomial growth, then for every $d$ the space of ...
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convergence of empirical distribution of random vectors

Given (a) random matrices $A^{n} \in \mathbb R^{n\times n}$ with iid normal entries $A_{ij}\sim \mathcal N(0, 1/n)$; and (b) $X^{n} \in \mathbb R^{n}$ with its empirical distributions converging ...
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When does equality occur in the triangle inequality in metric space? [on hold]

When I think of R^n , n<=3 ; it is very easy given the usual metric. But what if the metric is not usual?
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Is there a name for this quantity between two distributions?

Let $f$ be a probability density on a compact domain $D$, and say that $x_1,\dots,x_n$ are samples from $f$. If we wanted to compute the Wasserstein distance between $f$ and the empirical ...
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Pairwise distance distribution for point clouds (normal distribution) [on hold]

I have a point cloud (2D for now) of $N$ normally distributed points (with a certain $\sigma$). My first question would be how the pairwise distance distribution looks (just by chance I discovered a ...
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Flat cohomology of an ordinary liftable Calabi-Yau threefold

Let $k$ be a perfect field of characteristic $p>0$ and consider an ordinary liftable Calabi-Yau threefold $X_{0}/k$. By this I mean that $H^{i}(X_{0},B_{X_{0}/k}^{j})=0$ for all $i\geq 0$ and ...
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biharmonic equation with L^1 data and Navier Condition

I am reading an article that, a section of it is mentioned below . I have some question about this section. I will ask my question after the section below. I am thanksed if some one could help me , ...
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Counting function for prime pair with bounded gaps between them

I'll start by noting that I am not at all an expert on number theory. However I do use it in a proof and would like your assistance if possible. Yitang Zhang breakthrough result established that ...
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How many different sums of parts of a vector

I hope this question isn't too basic for MO. I also asked it on math.se previously. This mathematical puzzle was given to me by a friend a while ago and I can't work out how to solve it. Does anyone ...
Eigenvalues of the sum of two matrices, where one is $B=\operatorname{diag}(1, 0,\dots,0)$
I know that given two matrices $A$ and $B$, estimating the eigenvalues of $A + B$ by the eigenvalues of $A$ and $B$ is generally a non-easy problem. In particular, there are some results for matrices ...