Some extensions of Pitman’s and Ray-Knight’s theorems for penalized Brownian motions and their local times, IV
نویسندگان
چکیده
We show that Pitman’s theorem relating Brownian motion and the BES(3) process, as well as the Ray-Knight theorems for Brownian local times remain valid, mutatis mutandis, under the limiting laws of Brownian motion penalized by a function of its one-sided maximum.
منابع مشابه
Exponential functionals of Brownian motion, II: Some related diffusion processes
This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and ...
متن کاملExtensions of Some Fixed Point Theorems for Weak-Contraction Mappings in Partially Ordered Modular Metric Spaces
The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.
متن کاملLarge deviations for the local and intersection local times of fractional Brownian motions
Large deviation principle for the non-linear functionals of non-Markovian models is a challenging subject. A class of such models are Gaussian processes. Among them, the fractional Brownian motions are perhaps the most important processes. In this talk, I will talk about some recent progress achieved in the large deviations for local times and intersection local times of fractional Brownian mot...
متن کاملar X iv : m at h / 98 02 04 5 v 1 [ m at h . PR ] 9 F eb 1 99 8 STOCHASTIC BIFURCATION MODELS
We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trot-ter and Ray-Knight theorems), and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.
متن کاملProbability Graduate Students Seminar Introduction to the theory of Brownian Local Times
Local Times of Brownian Motion were introduced in 1948 by French mathematician Paul Lévy in his fundamental book Processus Stochastiques et Mouvement Brownien. Naturally arising in many problems (such as, for instance, an extension of Itô’s formula to convex functions, or finding the density of the occupation measure of BM with respect to the Lebesgue measure), they also roughly describe the am...
متن کامل