Strong invariance principle for singular di$usions
نویسنده
چکیده
We study a singular di$usion on Euclidean space which is characterized by the solution of a classical Itô stochastic di$erential equation in which the di$usion coe2cient is not necessarily of full rank. Our motivation is in earlier results of Basak (J. Multivariate Anal. 39 (1991) 44) and Basak and Bhattacharya (Ann. Probab. 20 (1992) 312), who establish su2cient conditions for singular di$usions to have a unique invariant probability and obtain a functional central limit theorem and functional law of the iterated logarithm for a large class of real-valued functions of the di$usion. Under similar conditions we establish a strong invariance principle for vector-valued functions of the di$usion, and use this to derive several asymptotic properties of the singular di$usion, including upper/lower-function estimates and a vector form of the functional law of the iterated logarithm. c © 2002 Elsevier Science B.V. All rights reserved. MSC: primary 60F17; secondary 60J60
منابع مشابه
Orientation Diiusions
100 Orientation di usions P. Perona Abstract|Di usions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, of analyzing images at multiple scales, and of enhancing discontinuities. A number of di usions of image brightness have been de ned and studied so far; they may be applied to scalar and vector-valued quantities that are natura...
متن کاملForward-Backward Stochastic Differential Equations Generated by Bernstein Diffusions
In this Note we present new results which bring about hitherto unknown relations between certain Bernstein di¤usions wandering in bounded convex domains of Euclidean space on the one hand, and processes which typically occur in forward-backward systems of stochastic di¤erential equations on the other hand. A key point in establishing such relations is the fact that the Bernstein di¤usions we co...
متن کاملA METHOD FOR COMPUTING DOUBLE BAND POLICIES FOR SWITCHING BETWEEN TWO DIFFUSIONS Revised Version March Running Title Optimal Switching Between Two Di usions
We develop a method for computing the optimal double band b B policy for switching between two di usions with continuous rewards and switch ing costs The two switch levels b B are obtained as perturbations of the single optimal switching point a of the control problem with no switching costs More precisely we nd that in the case of average reward problems the optimal switch levels can be obtain...
متن کاملComparison of time-inhomogeneous Markov processes
Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their in nitesimal generators as well as an invariance property of one process is assumed. The corresponding proof is based on a representation result for the solutions of inhomo...
متن کاملLarge Deviations for Non-Markovian Di↵usions and a Path-Dependent Eikonal Equation
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...
متن کامل