Simulating Brownian Motion and Related Processes
1 Simulating Brownian motion (BM) and geometric Brownian motion (GBM)
... (By convention if tk is not an integer then we replace it by the largest integer less than or equal to it; denoted by [tk].) This leads to the particle taking many many iid steps, but ea[r] ...
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Occupation densities for certain processes related to fractional Brownian motion
... 90, rue de Tolbiac, 75634 Paris Cedex 13, France. January 22, 2008 Abstract In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we ...
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Conditional characteristic functions of processes related to fractional Brownian motion
... For a broad class of stochastic processes, in particular affine models (see e.g. Duffie [4] and Duffie, Filipovic and Schachermayer [5]), such predictions are easy to calculate and do only depend on the level of ...
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Extremal Processes in Branching Brownian Motion and Friends
... branching Brownian motion [4, 1] and branching random walk ...The processes appearing here, Poisson point processes with random intensity (Cox pro- cesses, see [10]) decorated by a cluster ...
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Long range dependent processes and fractional Brownian motion
... dependent processes to financial m ...by Brownian m otion are a powerful tool used to describe the m ovem ent of stock ...because Brownian m otion is a Gaussian process with the m artingale property, ...
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Brownian motion and Levy processes on locally compact groups
... It is shown that every L´evy process on a locally compact group G is determined by a sequence of one-dimensional Brownian motions and an independent Poisson random measure. As a conse- quence, we are able to give ...
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Hurst exponents, Markov processes, and fractional Brownian motion
... paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H ≠ 1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case ...
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Time since maximum of Brownian motion and asymmetric Lévy processes
... the Brownian motion is that it is considerably harder to obtain analytical ...two related pieces, one dependent on t and the other on T − ...evy processes—at least in the special case of jumps ...
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Brownian motion vs. pure-jump processes for individual stocks
... Our approach allows to investigate the presence of jumps of infinite activity. This is not the case for the nonparametric approach using recent bipower variations (BPV) mea- sures proposed in Barndorff-Nielsen and ...
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Simulating Stock Prices Using Geometric Brownian Motion: Evidence from Australian Companies
... geometric Brownian motion observed in these charts tends to follow a slight upward trend which prices of stocks don’t tend to deviate significantly from this ...
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A strong uniform approximation of fractional Brownian motion by means of transport processes
... of processes that converges strongly to fractional Brownian motion uniformly on bounded intervals for any Hurst parameter H, and we derive a rate of convergence, which becomes better when H ...
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Is the Driving Force of a Continuous Process a Brownian Motion or Fractional Brownian Motion?
... a Brownian motion is typically used in modeling the asset prices, interest rates and ex- change rates, and so ...of Brownian motion as a driving force of the underlying asset price ...
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Macroscopic anisotropic Brownian motion is related to the directional movement of a “Universe field”
... ABSTRACT Brownian motion was discovered by the botan- ist Robert Brown in 1827, and the theoretical model of Brownian motion has real-world ap- plications in fields such as mathematics, eco- ...
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Stochastic Processes and Advanced Mathematical Finance. The Definition of Brownian Motion and the Wiener Process
... terms Brownian motion and Wiener process are the same, although Brownian motion emphasizes the physical aspects and Wiener process emphasizes the mathematical ...
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CiteSeerX — The fractional Brownian motion
... Proof. For t ∈ R, it follows from Theorem 3.1, that lim s→∞ EZ t H,s −Z t H 2 = 0. Hence, for all t, t ′ ∈ R, we have that EZ t H · Z t H ′ = lim s→∞ EZ t H,s · Z t H,s ′ = 1 2 |t| 2H + |t ′ | 2H − |t − t ′ | 2H ...
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Brownian motion and the distance to a submanifold
... The concentration inequality is derived using moment estimates to obtain an exponential bound, which holds under fairly general assumptions and which is sufficiently sharp to imply a comparison theorem. We provide ...
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On the Lifetime of a Conditioned Brownian Motion
... of Brownian motion, though it is still far from being rigorous from the stochastic point of ...results related to our studies are presented, trying to give a general context to the present ...
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The fractal geometry of Brownian motion
... of convergence, and related concepts. When we formulate the basic concepts of nonstandard analysis, we shall see that it too discriminates between different rates of convergence. Hausdorff amusingly called the ...
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BROWNIAN MOTION 1. INTRODUCTION
... stochastic processes behave, at least for long stretches of time, like random walks with small but frequent ...such processes will look, at least approximately, and on the appropriate time scale, like ...
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Arbitrage with fractional brownian motion?
... Remark. In [19] the notion of a market observer was introduced by Øksendal in order to justify the use of the Wick product in the self-financing condition. Roughly speaking, all formulae containing Wick products are in- ...
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