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      All Questions

      1
      vote
      0answers
      79 views

      Hashed coupon collector

      The story: A sport card store manager has $r$ customers, that together wish to assemble a $n$-cards collection. Every day, a random customer arrives and buys his favorite card (that is, each customer ...
      1
      vote
      0answers
      35 views

      Distribution of a linear pure-birth process's integral

      I stumbled across the following random variable, defined as the integral of a linear pure-birth process i.e. a Yule process: $$ Z_t = \mathbb{E}\bigg[\int_0^t Y_s ds \bigg| Y_t=k \bigg] $$ where $(...
      6
      votes
      1answer
      80 views

      The distribution of the area of a region cut out by chordal SLE?

      Let $\mathbb{D}$ be the unit disc. Let $a,b \in \partial \mathbb{D}$. Let $\gamma$ be a chordal $SLE_{k}$ from $a$ to $b$. For $k \leq 4$, $\gamma$ is a simple curve, and so $\mathbb{D} \setminus \...
      2
      votes
      0answers
      50 views

      Defining weak solutions to infinitely many SDEs on the same probability space

      Suppose I have an SDE of the form $$dX_t=b(X_t)dt+\sigma (X_t)dB_t+\int_{\mathbb{R}}G_{t-}(y)N(dtdy)$$ which I can solve weakly if I cut off the last integral to range over the set $\{\mid{y}\mid > ...
      0
      votes
      0answers
      103 views

      An application of Girsanov's Theorem

      Let $(W,H,i)$ be the classical Wiener space where $W=C_0([0,1])$, $H$ is the Cameron-Martin space. Let $A= I_{W}+a$ such that $A:W \rightarrow W$ and $a \in L^{0}(\mu,H)$, $a$ has adapted derivative, ...
      6
      votes
      1answer
      150 views

      Maxima of Brownian motion

      It is well-known that Brownian motion attains infinitely many maxima in each time interval $[0,T]$ a.s.. From a physics perspective it seems reasonable that when the disorder of the path of a ...
      2
      votes
      0answers
      61 views

      How to obtain mathematical expectation with the vector as random variable?

      In my study, I wish to get the mathematical expectation for the term below. The vector $\boldsymbol{z} \in \mathcal{C}^{N\times1}$ and $\boldsymbol z \sim \mathcal{CN}\left(\boldsymbol{0},\boldsymbol{...
      0
      votes
      1answer
      82 views

      Obtaining a lower bound on the expectation using the Sudakov-Fernique inequality

      In my work I wish to obtain a lower bound for the term below. Here the expectation is taken over $h$, a standard random Gaussian vector of length $n$. The minimum is taken over all $\{i_1,\dots,i_L\} \...
      0
      votes
      2answers
      79 views

      Lower bounds on discrete time finite Markov chains hitting probabilities

      I am interested in some general theorems related to lower bounds on discrete time finite Markov chains hitting probabilities (preferably ergodic chains , but not necessarily ), with references . ...
      3
      votes
      0answers
      42 views

      Random Two-Player Asymmetric Game

      About half a year ago I asked a question on MSE about a random two player game. At the time, the question received some attention and some progress was made, but was not resolved completely. I have ...
      3
      votes
      1answer
      83 views

      Total offspring of Poisson multitype branching process

      A normal branching process $Z_n$ initialized with $Z_0=1$ and offspring generated from $Pois(p),p<1,$ has a total progeny / total off spring distribution $$X=\sum_{n=0}^\infty Z_n$$ $X\in \mathbb{...
      2
      votes
      1answer
      81 views

      Heavy tail central limit theorem

      I am looking for a proof based on characteristic functions for the generalized central limit theorem when the second moment does not exist, in which case one ends up with a power law rather than a ...
      4
      votes
      1answer
      194 views

      A balls into bins problem with combinatorial constraints

      We are given $m$ balls and $n$ bins, with $m \ge n$. Each bin can contain at most $c$ balls (we assume that $c$ is an even integer). In a sequential fashion, at each time step, one ball is placed into ...
      0
      votes
      0answers
      26 views

      A modification of Kolmogorov's continuity criterion for $C_{tem}$

      I am wondering about how to prove a modification of Kolmogrov's continuity criterion in order to also being able to quantify the growth behaviour of the process. In particular, I am interested in the ...
      3
      votes
      0answers
      69 views

      Convergence rate of the smallest eigenvalue of an integral of a multivariate squared Brownian Motion

      I am interested in deriving the convergence rate of the smallest eigenvalue of a sequence of random matrices with diverging dimension. More precisely, let $W_n(r)$ represent an $n$-dimensional ...

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