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In this paper, we show how to exactly sample from the distribution of the maximum of a random walk with negative drift. We also explore related variance reduction methods.
Considera random walk S=(Sn:n≥O) that is "perturbed" by a stationary sequence (ξn:n≥O) to produce the process S=(Sn+ξn:n≥O). In this paper, we are concerned with developing limit theorems and approxim...
Consider a random walk S = (Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time ma...
Consider a random walk (Sn: n ≥ 0) with drift −μ and S0= 0. Assuming that the increments have exponential moments, negative mean, and are strongly nonlattice, we provide a complete asymptotic ex...
This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with va...
We study the statistics of records of a one-dimensional random walk of nsteps,starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of lengt...
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like , where t is time, Q(s) is the value of a stochastic proc...
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time se...
I met Peter J. Bickel for the first time in 1981. He came to Jerusalem for a year; I had just started working on my Ph.D. studies.
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion ...
By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it d...
Let (Bt)0tT be either a Bernoulli random walk or a Brownian motion with drift, and let Mt := max{Bs : 0  s  t}, 0  t  T. This paper solves the general optimal prediction problem sup 0T E[f(MT...
Given a Harris chain (M,,)n40 on any state space (9C,) with essentially unique stationary measure <, let (Xn)nZObe a sequence of real-valued random variables which are conditionally independent, gi...
In the present paper we consider a continuous time random walk on an anisotropic random lattice. We show the existence of a steady state 0, for the environment process (( (t)),ao corresponding to t...
In this paper, we consider some distributions of maxima of excursions and related variables for standard random walk and Brownian motion. We discuss the infinite divisibility properties of these di...

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