Results 11 to 20 of about 908 (31)
On the most visited sites of planar Brownian motion [PDF]
, 2012 Let (B_t : t > 0) be a planar Brownian motion and define gauge functions $\phi_\alpha(s)=log(1/s)^{-\alpha}$ for $\alpha>0$. If $\alpha 0 : B_t=x})>0$, but if $\alpha>1$ almost surely $H^{\phi_\alpha} ({t > 0 : B_t=x})=0$ simultaneously for all $x\in R^2$
Cammarota, Valentina, Mörters, Peter
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Generalized Bessel function of Type D [PDF]
, 2008 We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.Comment: This is a ...
Demni, Nizar
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, 2016 Let $M_r$ be the maximum value of an one-dimensional Brownian motion on the (time) interval $[0, r]$. We derive an explicit formula for the distribution of the time required (after $r$) for the Brownian motion to exceed $M_r$.Comment: 3 ...
Papanicolaou, Vassilis G.
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A probabilistic solution to the Stroock-Williams equation [PDF]
, 2014 We consider the initial boundary value problem \begin{eqnarray*}u_t=\mu u_x+\tfrac{1}{2}u_{xx}\qquad (t>0,x\ge0),\\u(0,x)=f(x)\qquad (x\ge0),\\u_t(t,0)=\nu u_x(t,0)\qquad (t>0)\end{eqnarray*} of Stroock and Williams [Comm. Pure Appl. Math. 58 (2005) 1116-
Peskir, Goran
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An embedding for the Kesten-Spitzer random walk in random scenery [PDF]
, 1998 For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis.
Csáki, Endre +2 more
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On the Moving Boundary Hitting Probability for the Brownian Motion [PDF]
, 2007 2000 Mathematics Subject Classification: 60J65.Consider the probability that the Brownian motion hits a moving two-sided boundary by a certain moment.
P. Kralchev, Dobromir
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Isoperimetric-type inequalities for iterated Brownian motion in R^n
, 2006 We extend generalized isoperimetric-type inequalities to iterated Brownian motion over several domains in $\RR{R}^{n}$. These kinds of inequalities imply in particular that for domains of finite volume, the exit distribution and moments of the first exit
Allouba +15 more
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Blending Brownian motion and heat equation
, 2015 In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with ...
Cristiani, Emiliano
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A note on a.s. finiteness of perpetual integral functionals of diffusions [PDF]
, 2005 In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions.
Salminen, Paavo, Yor, Marc
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Sharp estimates of the spherical heat kernel
, 2018 We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.Comment: 9 pages, to appear in J. Math.
Nowak, Adam +2 more
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