共查询到20条相似文献,搜索用时 15 毫秒
1.
Peter Hieber 《Statistics & probability letters》2012,82(1):165-172
The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model is to introduce a stochastic time scale. This equips the modelled returns with desirable stylized facts such as volatility clusters and jumps. For continuous time transformations, independent of the Brownian motion, we show that analytical results for the double-barrier problem can be obtained via the Laplace transform of the time change. The result is a very efficient power series representation for the resulting exit probabilities. We discuss possible specifications of the time change based on integrated intensities of shot-noise type and of basic affine process type. 相似文献
2.
We study Brownian motion reflected on an ``independent' Brownian path. We prove results on the joint distribution of both
processes and the support of the parabolic measure in the space-time domain bounded by a Brownian path. We show that there
exist two different natural local times for a Brownian path reflected on a Brownian path.
Received: 25 October 2000 / Revised version: 30 March 2001 / Published online: 20 December 2002 相似文献
3.
E. Michael 《Topology and its Applications》2011,158(13):1526-1528
Principal result: Suppose Y is metrizable. Then: (a) if X is metrizable and A⊂X is closed, then every continuous g:A→Y extends to an l.s.c. ψ:X→K(Y); (b) Y satisfies (a) for all paracompact X if and only if Y is completely metrizable. 相似文献
4.
B. Davvaz 《Journal of Applied Mathematics and Computing》2003,11(1-2):265-271
The purpose of this paper is to present certain results arising from product between fuzzyH v -submodules. In particular, we consider the fundamental relatione * defined on anH v -module and give a property of the fundamental relations and fundamental modules with respect to the fuzzy product ofH v -modules. 相似文献
5.
《Applied Mathematics Letters》2002,15(2):193-196
In this note, we first define the concept of convex fuzzy processes. Second, we present some basic properties of convex fuzzy processes and important connection between convex fuzzy processes and their graphs. 相似文献
6.
We study the effect of the forcing term to the solution of a fuzzy differential equation. 相似文献
7.
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at \(-\infty \) . We show that these processes do not have to have the distribution of standard Brownian motion in the backward direction of time, no matter which random time we take as the origin. We study the maximum and minimum rates of growth for these processes in the backward direction. We also address the question of which extra assumptions make one of these processes a two-sided Brownian motion. 相似文献
8.
Domenico Candeloro Coenraad C. A. Labuschagne Valeria Marraffa Anna Rita Sambucini 《Ricerche di matematica》2018,67(2):347-360
Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach spaces X. The present paper is an application of the paper (Labuschagne et al. in Quaest Math 30(3):285–308, 2007) in which an embedding result is obtained which considers also the ordered structure of the family of compact convex subsets of a Banach space X and of Grobler and Labuschagne (J Math Anal Appl 423(1):797–819, 2015; J Math Anal Appl 423(1):820–833, 2015) in which these processes are considered in f-algebras. Moreover, in the space of continuous functions defined on a Stonian space, a direct Levy’s result follows. 相似文献
9.
Let B be a fractional Brownian motion with Hurst index H(0,1). Denote by the positive, real zeros of the Bessel function J–H of the first kind of order –H, and let be the positive zeros of J1–H. In this paper we prove the series representation where X1,X2,... and Y1,Y2,... are independent, Gaussian random variables with mean zero and and the constant cH2 is defined by cH2=–1(1+2H) sin H. We show that with probability 1, both random series converge absolutely and uniformly in t[0,1], and we investigate the rate of convergence.Mathematics Subject Classification (2000): 60G15, 60G18, 33C10 相似文献
10.
Jean Bertoin 《Probability Theory and Related Fields》2000,117(2):289-301
Let (B
s
, s≥ 0) be a standard Brownian motion and T
1 its first passage time at level 1. For every t≥ 0, we consider ladder time set ℒ
(t)
of the Brownian motion with drift t, B
(t)
s
= B
s
+ ts, and the decreasing sequence F(t) = (F
1(t), F
2(t), …) of lengths of the intervals of the random partition of [0, T
1] induced by ℒ
(t)
. The main result of this work is that (F(t), t≥ 0) is a fragmentation process, in the sense that for 0 ≤t < t′, F(t′) is obtained from F(t) by breaking randomly into pieces each component of F(t) according to a law that only depends on the length of this component, and independently of the others. We identify the fragmentation
law with the one that appears in the construction of the standard additive coalescent by Aldous and Pitman [3].
Received: 19 February 1999 / Revised version: 17 September 1999 /?Published online: 31 May 2000 相似文献
11.
《Fuzzy Sets and Systems》1987,23(3):393-397
Lowen introduced the concept of fuzzy neighbourhood spaces (fns's), and proved that the family of level topologies of a fns is an antichain. Wuyts characterized fns's as being those fully stratified fuzzy topological spaces (fts's) whose level topologies form antichains and whose fuzzy topologies are the finest possible for thier level topologies. Mashhour et al. introduced the axiom of structure A on fts's, and derived for it several characterizations and fuzzy topological consequences. We use those characterizations of structure A and Wuyts' characterization of fns's to prove that a fts is a fns iff it is of structure A and fully stratified. 相似文献
12.
Rudolf Kruse 《Fuzzy Sets and Systems》1982,8(2):219-222
A relation between λ-additive fuzzy measures and measures is given. This relation is used to prove some properties of λ-additive fuzzy measures. 相似文献
13.
Brownian motion on the continuum tree 总被引:1,自引:1,他引:0
W. B. Krebs 《Probability Theory and Related Fields》1995,101(3):421-433
Summary We construct Brownian motion on a continuum tree, a structure introduced as an asymptotic limit to certain families of finite trees. We approximate the Dirichlet form of Brownian motion on the continuum tree by adjoining one-dimensional Brownian excursions. We study the local times of the resulting diffusion. Using time-change methods, we find explicit expressions for certain hitting probabilities and the mean occupation density of the process. 相似文献
14.
Brownian motion on the Sierpinski gasket 总被引:11,自引:0,他引:11
Summary We construct a Brownian motion taking values in the Sierpinski gasket, a fractal subset of 2, and study its properties. This is a diffusion process characterized by local isotropy and homogeneity properties. We show, for example, that the process has a continuous symmetric transition density, p
t(x,y), with respect to an appropriate Hausdorff measure and obtain estimates on p
t(x,y).Research partially supported by an NSERC of Canada operating grantResearch partially supported by an SERC (UK) Visiting Fellowship 相似文献
15.
Any solution of the functional equation
where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an α-perturbed
reflected Brownian motion. Similarly any solution of
behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an α,β-doubly perturbed Brownian
motion. We complete some recent investigations by showing that for all permissible values of the parameters α, α and β respectively,
these equations have pathwise unique solutions, and these are adapted to the filtration of B.
Received: 7 November 1997 / Revised version: 13 July 1998 相似文献
16.
Summary. We study the asymptotic behavior of Brownian motion and its conditioned process in cones using an infinite series representation
of its transition density. A concise probabilistic interpretation of this series in terms of the skew product decomposition
of Brownian motion is derived and used to show properties of the transition density.
Received: 2 April 1996 / In revised form: 21 December 1996 相似文献
17.
18.
19.
Summary. Hyperbolic branching Brownian motion is a branching diffusion process in which individual particles follow independent Brownian
paths in the hyperbolic plane ?
2
, and undergo binary fission(s) at rate λ > 0. It is shown that there is a phase transition in λ: For λ≦ 1/8 the number of particles in any compact region of ?
2
is eventually 0, w.p.1, but for λ > 1/8 the number of particles in any open set grows to ∞ w.p.1. In the subcritical case (λ≦ 1/8) the set Λ of all limit points in ∂?
2
(the boundary circle at ∞) of particle trails is a Cantor set, while in the supercritical case (λ > 1/8) the set Λ has full Lebesgue measure. For λ≦ 1/8 it is shown that w.p.1 the Hausdorff dimension of Λ is δ = (1−√1−8 λ)/2.
Received: 2 November 1995 / In revised form: 22 October 1996 相似文献
20.