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pro vyhledávání: '"Ernst, Philip A."'
Let $M(n, k, p)$ denote the maximum probability of the event $X_1 = X_2 = \cdots = X_n=1$ under a $k$-wise independent distribution whose marginals are Bernoulli random variables with mean $p$. A long-standing question is to calculate $M(n, k, p)$ fo
Externí odkaz:
http://arxiv.org/abs/2407.18688
Autor:
Ernst, Philip A., Peskir, Goran
The Gapeev-Shiryaev conjecture (originating in Gapeev and Shiryaev (2011) and Gapeev and Shiryaev (2013)) can be broadly stated as follows: Monotonicity of the signal-to-noise ratio implies monotonicity of the optimal stopping boundaries. The conject
Externí odkaz:
http://arxiv.org/abs/2405.01685
Autor:
Ernst, Philip, Stolyar, Alexander
We revisit a classical problem in dynamic storage allocation. Items arrive in a linear storage medium, modeled as a half-axis, at a Poisson rate $r$ and depart after an independent exponentially distributed unit mean service time. The arriving item s
Externí odkaz:
http://arxiv.org/abs/2404.03797
Autor:
Ernst, Philip, Mei, Hongwei
Consider the sample path of a one-dimensional diffusion for which the diffusion coefficient is given and where the drift may take on one of two values: $\mu_0$ or $\mu_1$. Suppose that the signal-to-noise ratio (defined as the difference between the
Externí odkaz:
http://arxiv.org/abs/2311.00137
Autor:
Ernst, Philip A., Huang, Dongzhou
This paper begins with a study of both the exact distribution and the asymptotic distribution of the empirical correlation of two independent AR(1) processes with Gaussian innovations. We proceed to develop rates of convergence for the distribution o
Externí odkaz:
http://arxiv.org/abs/2310.08575
Consider the motion of a Brownian particle in $n$ dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, exactly $k$ of the coordinate processes get a (known) non-zer
Externí odkaz:
http://arxiv.org/abs/2305.05721
Publikováno v:
The Oxford Companion to the Book, 1 ed., 2010.
Externí odkaz:
http://www.oxfordreference.com/view/10.1093/acref/9780198606536.001.0001/acref-9780198606536-e-2003
Publikováno v:
In Nonlinear Analysis: Hybrid Systems August 2024 53
Autor:
Ernst, Philip, Mei, Hongwei
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has discontinuous paths
Externí odkaz:
http://arxiv.org/abs/2107.14441
We consider the Brownian ``spider process'', also known as Walsh Brownian motion, first introduced in the epilogue of Walsh 1978. The paper provides the best constant $C_n$ for the inequality $$ E D_\tau\leq C_n \sqrt{E \tau},$$ where $\tau$ is the c
Externí odkaz:
http://arxiv.org/abs/2105.15202