共查询到20条相似文献,搜索用时 46 毫秒
1.
David G. Hobson 《Statistics & probability letters》2013,83(10):2386-2390
We construct a fake exponential Brownian motion, a continuous martingale different from classical exponential Brownian motion but with the same marginal distributions, thus extending results of Albin and Oleszkiewicz for fake Brownian motions. The ideas extend to other diffusions. 相似文献
2.
本文研究了一维扩散过程的最优停止问题,论证了W iener过程和几何布朗运动是F e ller过程,同时给出了一般扩散过程的处理方法. 相似文献
3.
Richard B. Sowers Jang-Mei Wu 《Transactions of the American Mathematical Society》1999,351(6):2553-2567
We consider the Allen-Cahn equation in a well-known scaling regime which gives motion by mean curvature. A well-known transformation of this PDE, using its standing wave, yields a PDE the solution of which is approximately the distance function to an interface moving by mean curvature. We give bounds on this last fact in terms of thermal capacity. Our techniques hinge upon the analysis of a certain semimartingale associated with a certain PDE (the PDE for the approximate distance function) and an analogue of some results by Bañuelos and Øksendal relating lifetimes of diffusions to exterior capacities.
4.
A. N. Borodin 《Journal of Mathematical Sciences》2008,152(6):840-852
The paper deals with some transformations of diffusions with jumps. We consider the class of diffusions with jumps that is
closed with respect to composition with invertible, twice continuously differentiable functions. A special random time change
gives us again a diffusion with jumps. A result on transformation of a measure is valid for this class of diffusions with
jumps. Bibliographty: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 79–100. 相似文献
5.
A Bose 《Journal of multivariate analysis》1983,13(3):442-463
We consider the problem of constructing entrance laws for Feller diffusions on the state space (0, ∞). Our method, based on Feller-McKean theory of one-dimensional diffusions, gives an analytic expression for the entrance density in terms of transition density. Moreover, the entrance density is the density of the first passage time to the left boundary {0}. Also, the entrance density is related to the transition density via Doob's h-path transformation. 相似文献
6.
Edwin Perkins 《Probability Theory and Related Fields》1992,94(2):189-245
Summary A strong equation driven by a historical Brownian motion is used to construct and characterize measure-valued branching diffusions in which the spatial motions obey an Itô equation with drift and diffusion depending on the position of an individual and the entire population. 相似文献
7.
《Comptes Rendus Mathematique》2002,334(12):1119-1124
We observed, in a previous work, that Brownian motion reflected on an independent time-reversed Brownian motion is again Brownian motion. We present the generalisation of this result to pairs of conjugate diffusions (which are also dual, in the sense of Siegmund). To cite this article: F. Soucaliuc, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1119–1124. 相似文献
8.
A. N. Borodin 《Journal of Mathematical Sciences》2011,176(2):146-161
The paper deals with methods of computation of distributions of integral functionals of diffusions with jumps at time moments
at which the maximal and minimal values of diffusions are achieved. As an example, we obtain closed-form expressions for the
Laplace transform of joint locations of the minimum and maximum of a process that equals the sum of a Brownian motion and
the compound Poisson process. Bibliography: 7 titles. 相似文献
9.
A well-known theorem by Spitzer states that the winding number of a standard Brownian motion around the origin is asymptotically Cauchy-distributed. A similar result is derived for positive recurrent diffusions in the plane given by a non-degenerate stochastic equation. 相似文献
10.
A binomial lattice approach is proposed for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log‐transformation of the underlying processes, which is step by step consistent with the continuous‐time diffusions, and a change of basis of the asset span, to transform asset prices into uncorrelated processes. An additional transformation is applied to approximate driftless dynamics. Even if these features are simple and straightforward to implement, it is shown that they significantly improve the efficiency of the multi‐dimensional binomial algorithm. A thorough test of efficiency is provided compared with most popular binomial and trinomial lattice approaches for multi‐dimensional diffusions. Although the order of convergence is the same for all lattice approaches, the proposed method shows improved efficiency. 相似文献
11.
In this paper, for homogeneous diffusion processes, the approach of Y. Li and X. Zhou [Statist. Probab. Lett., 2014, 94: 48–55] is adopted to find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (-∞, α) and (α, ∞): The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions for Brownian motion with drift, skew Brownian motion, and Brownian motion with two-valued drift, respectively. 相似文献
12.
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our
test is based on discrete time observation of the processes, and the diffusion coefficient is a nuisance function which is
“estimated” in some sense in our testing procedure. We prove that the limit distribution of our test is the supremum of the
standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent
under any fixed alternative. 相似文献
13.
M. Weber 《Mathematische Nachrichten》1992,157(1):65-75
A class of infinitesimal generators A of strongly continuous nonnegative contraction semigroups in a subspace of C[0, 1] is introduced. It contains the class of generators of regular gap diffusions. A construction of the Markov process X generated by A gives some stochastic interpretations of the integral term which appears in A. The infinitesimal generator of the time reversal of X (with respect to its life time) is explicitly given. It belongs to the introduced class of generators too. Thus, the considered class is invariant under this transformation. Two examples, the time reversal of gap diffusions with nonlocal boundary conditions and the time reversal of processes with Levy-measure, complete the note. 相似文献
14.
Hardeep S. Gill 《Stochastic Processes and their Applications》2009,119(12):3981-4003
We construct a class of interactive measure-valued diffusions driven by a historical super-Brownian motion and an independent white noise by solving a certain stochastic equation. In doing so, we show that the approach of Perkins (2002) [3] can be used to study the problem examined by Dawson et al. (2001) [1]. This unifies and extends both Dawson et al. (2001) [1] and Perkins (2002) [3] and establishes a new class of measure-valued diffusions. The existence and pathwise uniqueness of the solutions are proved, and the solutions are shown to satisfy the natural martingale problem. 相似文献
15.
A. N. Borodin 《Journal of Mathematical Sciences》2010,167(4):474-485
The paper deals with methods of computation of distributions of location for maxima and minima for diffusions with jumps.
As an example, we obtain explicit formulas for distributions of location for the maximum of the process which is equal to
the sum of a Brownian motion and the compound Poisson process. Bibliography: 8 titles. 相似文献
16.
Asymptotically one-dimensional diffusions on the Sierpinski gasket constitute a one parameter family of processes with significantly different behaviour to the Brownian motion. Due to homogenization effects they behave globally like the Brownian motion, yet locally they have a preferred direction of motion. We calculate the spectral dimension for these processes and obtain short time heat kernel estimates in the Euclidean metric. The results are derived using branching process techniques, and we give estimates for the left tail of the limiting distribution for a supercritical multi-type branching process with varying environment. 相似文献
17.
Abstract
In author’s one previous paper, the same topic was studied
for one dimensional diffusions. As a continuation, this paper
studies the discrete case, that is the birth-death processes.
The explicit criteria for the inequalities, the variational
formulas and explicit bounds of the corresponding constants in
the inequalities are presented. As typical applications, the
Nash inequalities and logarithmic Sobolev inequalities are
examined.
Research supported in part by NSFC (No. 10121101),
973 Project and RFDP 相似文献
18.
The filtering of diffusions from their noisy observations is considered in this paper. The introduction of various reference probability measures and the use of a stochastic Feynman-Kac formula is shown to lead to new and already known filtering equations. In some cases, which include extensions of the Benes filtering problem, the new equations we propose possess a nice Gaussian solution, yielding an explicit finite dimensional filter 相似文献
19.
《Stochastic Processes and their Applications》2004,111(1):57-76
We establish a representation formula for the transition probability density of a diffusion perturbed by a vector field, which takes a form of Cameron–Martin's formula for pinned diffusions. As an application, by carefully estimating the mixed moments of a Gaussian process, we deduce explicit, strong lower and upper estimates for the transition probability function of Brownian motion with drift of linear growth. 相似文献
20.
We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.Mathematics Subject Classification (2000):Primary 60G17, 60J60, Secondary 28A80, 30C35, 60G52, 60J50 相似文献